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- PERGAMON-ELSEVIER SCIENCE LTD
- Biblioteca Digitais de Teses e Dissertações da USP
- Biblioteca Digital da Unicamp
- Universidade de Adelaide
- Universidade Federal de Pelotas; Faculdade de Educação; Programa de Pós-Graduação em Ensino de Ciências e Matemática; UFPel; Brasil
- Universidade Nacional da Austrália
- Universidade Cornell
- Elsevier
- Mais Publicadores...

## An algorithm for automatic checking of exercises in a dynamic geometry system: iGeom

Fonte: PERGAMON-ELSEVIER SCIENCE LTD
Publicador: PERGAMON-ELSEVIER SCIENCE LTD

Tipo: Artigo de Revista Científica

ENG

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#dynamic geometry#automatically checking exercises#distance education#geometry#iGeom#Computer Science, Interdisciplinary Applications#Education & Educational Research

One of the key issues in e-learning environments is the possibility of creating and evaluating exercises. However, the lack of tools supporting the authoring and automatic checking of exercises for specifics topics (e.g., geometry) drastically reduces advantages in the use of e-learning environments on a larger scale, as usually happens in Brazil. This paper describes an algorithm, and a tool based on it, designed for the authoring and automatic checking of geometry exercises. The algorithm dynamically compares the distances between the geometric objects of the student`s solution and the template`s solution, provided by the author of the exercise. Each solution is a geometric construction which is considered a function receiving geometric objects (input) and returning other geometric objects (output). Thus, for a given problem, if we know one function (construction) that solves the problem, we can compare it to any other function to check whether they are equivalent or not. Two functions are equivalent if, and only if, they have the same output when the same input is applied. If the student`s solution is equivalent to the template`s solution, then we consider the student`s solution as a correct solution. Our software utility provides both authoring and checking tools to work directly on the Internet...

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## "Desenvolvimento de ferramentas no iGeom: utilizando a geometria dinâmica no ensino presencial e a distância" ; "Developing tools in iGeom: Using the dynamic geometry in the classroom and distance learning"

Fonte: Biblioteca Digitais de Teses e Dissertações da USP
Publicador: Biblioteca Digitais de Teses e Dissertações da USP

Tipo: Dissertação de Mestrado
Formato: application/pdf

Publicado em 01/04/2005
PT

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#distance learning#dynamic geometry#ensino a distância#geometria dinâmica#informática na educação#informatics in education

Neste trabalho, apresentamos o desenvolvimento de ferramentas no programa iGeom - Geometria Interativa na Internet, para ensino-aprendizagem de Geometria, dando destaque aos recursos que facilitam a integração e uso deste programa, principalmente em ambientes de educação a distância via Internet. Atualmente, este tipo de programa é bastante conhecido e a Geometria que ele possibilita é usualmente denominada Geometria Dinâmica. Em poucas palavras, um programa de Geometria Dinâmica é a implementação computacional da régua e do compasso, permitindo que os objetos construídos sejam movidos mantendo-se às propriedades da construção. Dentre os principais recursos desenvolvidos, destacamos a autoria e a validação automática de exercícios e a comunicação com servidores, que podem ser utilizados para integrarem o iGeom em sistemas gerenciadores de cursos pela Web. Deste modo, se integrado a um sistema gerenciador, estes recursos podem ser utilizados para facilitar a tarefa do professor, que poderá criar exercícios diretamente pela Web e não precisará avaliar pessoalmente as respostas de cada aluno, e também para que o aluno saiba de imediato se sua solução está dentro do esperado pelo professor.¶; In this work...

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## Geometria diferencial em grupos de Lie; Differential geometry on Lie groups

Fonte: Biblioteca Digital da Unicamp
Publicador: Biblioteca Digital da Unicamp

Tipo: Dissertação de Mestrado
Formato: application/pdf

Publicado em 02/05/2013
PT

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#Geometria diferencial#Lie#Grupos de#Geometria riemaniana#Curvatura#Differential geometry#Groups#Lie#Riemannian geometry#Curvatura

Neste trabalho estudamos os aspectos geométricos dos grupos de Lie do ponto de vista da geometria Riemanniana, geometria Hermitiana e geometria Kähler, através das estruturas geométricas invariantes associadas. Exploramos resultados relacionados às curvaturas da variedade Riemanniana subjacente a um grupo de Lie através do estudo de sua álgebra de Lie correspondente. No contexto da geometria Hermitiana e geometria Kähler, para um caso concreto de grupo de Lie complexo, investigaram suas curvaturas seccionais holomorfas e verificamos a existência de uma estrutura pseudo-Kähler invariante por sua forma real compacta.; In this dissertation, we study the geometric aspects of Lie groups from the viewpoint of Riemannian geometry, Hermitian geometry, and Kähler geometry through its associated invariant geometric structures. We explore results related to curvatures of Riemannian manifold underlying a Lie group by studying its corresponding Lie algebra. In the context of Hermitian geometry and Kähler geometry, for a complex Lie group case, we investigate its holomorphic sectional curvatures and verify the existence of pseudo-Kähler structure invariant for its compact real form.

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## Generalized geometry

Fonte: Universidade de Adelaide
Publicador: Universidade de Adelaide

Tipo: Tese de Doutorado
Formato: 730723 bytes; 54917 bytes; application/pdf; application/pdf

Publicado em //2007
EN

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Generalized geometry is a recently discovered branch of differential geometry that has received a reasonable amount of interest due to the emergence of several connections with areas of Mathematical Physics. The theory is also of interest because the different geometrical structures are often generalizations of more familiar geometries. We provide an introduction to the theory which explores a number of these generalized geometries. After introducing the basic underlying structures of generalized geometry we look at integrability which offers some geometrical insight into the theory and this leads to Dirac structures. Following this we look at generalized metrics which provide a generalization of Riemannian metrics. We then look at generalized complex geometry which is a generalization of both complex and symplectic geometry and is able to unify a number of features of these two structures. Beyond generalized complex geometry we also look at generalized Calabi-Yau and generalized Kähler structures which are also generalizations of the more familiar structures.; Thesis (M.Sc.(M&CS))--University of Adelaide, School of Mathematical Sciences, Discipline of Pure Mathematics, 2007.

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## A Geometria da escola e a utilização de história em quadrinhos nos anos finais do Ensino Fundamental; The Geometry of the school and the using cartoons in the final years of primary school

Fonte: Universidade Federal de Pelotas; Faculdade de Educação; Programa de Pós-Graduação em Ensino de Ciências e Matemática; UFPel; Brasil
Publicador: Universidade Federal de Pelotas; Faculdade de Educação; Programa de Pós-Graduação em Ensino de Ciências e Matemática; UFPel; Brasil

Tipo: Dissertação de Mestrado

POR

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#Educação#Matemática#História da matemática#História em quadrinhos#Ensino da geometria#Education#Mathematics#History of mathematics#Comics#Teaching geometry#CNPQ::CIENCIAS HUMANAS::EDUCACAO

This study deals with a qualitative investigation with quantitative aspects carried out
during 2012 and 2013. It aims to learn about the reality of Geometry teaching in the
final years of primary school in the municipal schools in the city of Pelotas in order to
provide the History of Mathematics as a mediating instrument for teaching and
learning through cartoons. The theoretical foundation is made up of three stages.
Firstly, the search of elements about the history of mathematics and cartoons as
pedagogical resources to be used in the classroom. The Scientific Electronic Library
Online (SciElO) dataset is used for free searches on the internet. It also uses the
approaches provided by Miguel (1997, 2009) as well as the ones provided by
Vergueiro (2010). In the second stage a bibliographic study, regarding the mediation
concepts, zone of proximal development, spontaneous and scientific knowledge
about Vygotsky theory (2011) and researchers in the area, was carried out. This
study was used in the elaboration of the product of this research. The third stage
resorts to Pavanello (1989) and to event publication datasets such as the National
Meeting of Mathematics Education in order to capture elements to understand the
teaching of Geometry in the schools. As far as the empirical field is concerned...

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## Lorentzian geometry and physics in Kasparov's theory

Fonte: Universidade Nacional da Austrália
Publicador: Universidade Nacional da Austrália

Tipo: Thesis (PhD)

EN

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We study two geometric themes, Lorentzian geometry and gauge theory, from the
perspective of Connes’ noncommutative geometry and (the unbounded version of)
Kasparov’s KK-theory. Lorentzian geometry is the mathematical framework underlying
Einstein’s description of gravity. The geometric formulation of a gauge theory
(in terms of principal bundles) offers a classical description for the interactions
between particles. The underlying motivation is the hope that this noncommutative
approach may lead to a unified description of gauge theories coupled with
gravity on a Lorentzian manifold.
The main objects in noncommutative geometry are spectral triples, which encompass
and generalise Riemannian spin manifolds. A spectral triple defines a
class in K-homology, via which one can access the topology of the (noncommutative)
manifold. In this thesis we present two possible definitions for ‘Lorentian
spectral triples’, which offer noncommutative generalisations of Lorentzian manifolds
as well. We will prove that both definitions preserve the link with analytic
K-homology. We will describe under which conditions Lorentzian (or pseudo-
Riemannian) manifolds satisfy these definitions. Another main example is the
harmonic oscillator...

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## Absolute Parallelism Geometry: Developments, Applications and Problems

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 17/09/2002

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Absolute parallelism geometry is frequently used for physical applications.
It has two main defects, from the point of view of applications. The first is
the identical vanishing of its curvature tensor. The second is that its
autoparallel paths do not represent physical trajectories. The present work
shows how these defects were treated in the course of development of the
geometry. The new version of this geometry contains simultaneous non-vanishing
torsion and curvatures. Also, the new paths discovered in this geometry do
represent physical trajectories. Advantages and disadvantages of this geometry
are given for each stage of its development. Physical applications are just
mentioned without giving any details.; Comment: 12 Pages Tex file. A version of this paper has been published in the
Proceeding of the 11th conference on "Finsler, Lagrange and Hamilton
Geometry", held in Romania (Bacau, Feb. 2000)

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## Generalized complex geometry

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

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#Mathematics - Differential Geometry#Mathematics - Algebraic Geometry#Mathematics - Symplectic Geometry#53C15, 53C80, 53D17

Generalized complex geometry, introduced by Hitchin, encompasses complex and
symplectic geometry as its extremal special cases. We explore the basic
properties of this geometry, including its enhanced symmetry group, elliptic
deformation theory, relation to Poisson geometry, and local structure theory.
We also define and study generalized complex branes, which interpolate between
flat bundles on Lagrangian submanifolds and holomorphic bundles on complex
submanifolds.; Comment: 49 pages, refined from math.DG/0401221 and updated with new
constructions, added references.

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## Azumaya noncommutative geometry and D-branes - an origin of the master nature of D-branes

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 19/12/2011

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#Mathematics - Algebraic Geometry#High Energy Physics - Theory#Mathematics - Differential Geometry#Mathematics - Symplectic Geometry

In this lecture I review how a matrix/Azumaya-type noncommutative geometry
arises for D-branes in string theory and how such a geometry serves as an
origin of the master nature of D-branes; and then highlight an abundance
conjecture on D0-brane resolutions of singularities that is extracted and
purified from a work of Douglas and Moore in 1996. A conjectural relation of
our setting with `D-geometry' in the sense of Douglas is also given. The
lecture is based on a series of works on D-branes with Shing-Tung Yau, and in
part with Si Li and Ruifang Song.; Comment: 23 pages, 5 figures; parts delivered in the workshop `Noncommutative
algebraic geometry and D-branes', December 12 -- 16, 2011, organized by
Charlie Beil, Michael Douglas, and Peng Gao, at Simons Center for Geometry
and Physics, Stony Brook University, Stony Brook, NY

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## The Hitchin Model, Poisson-quasi-Nijenhuis Geometry and Symmetry Reduction

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

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We revisit our earlier work on the AKSZ formulation of topological sigma
model on generalized complex manifolds, or Hitchin model. We show that the
target space geometry geometry implied by the BV master equations is
Poisson--quasi--Nijenhuis geometry recently introduced and studied by Sti\'enon
and Xu (in the untwisted case). Poisson--quasi--Nijenhuis geometry is more
general than generalized complex geometry and comprises it as a particular
case. Next, we show how gauging and reduction can be implemented in the Hitchin
model. We find that the geometry resulting form the BV master equation is
closely related to but more general than that recently described by Lin and
Tolman, suggesting a natural framework for the study of reduction of
Poisson--quasi--Nijenhuis manifolds.; Comment: 38 pages, no figures, LaTex. One paragraph in sect. 6 and 3
references added

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## Gromov compactness in non-archimedean analytic geometry

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

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Gromov's compactness theorem for pseudo-holomorphic curves is a foundational
result in symplectic geometry. It controls the compactness of the moduli space
of pseudo-holomorphic curves with bounded area in a symplectic manifold.
In this paper, we prove the analog of Gromov's compactness theorem in
non-archimedean analytic geometry. We work in the framework of Berkovich
spaces.
First, we introduce a notion of K\"ahler structure in non-archimedean
analytic geometry using metrizations of virtual line bundles. Second, we
introduce formal stacks and non-archimedean analytic stacks. Then we construct
the moduli stack of non-archimedean analytic stable maps using formal models,
Artin's representability criterion and the geometry of stable curves. Finally,
we reduce the non-archimedean problem to the known compactness results in
algebraic geometry. The motivation of this paper is to provide the foundations
for non-archimedean enumerative geometry.; Comment: Improved presentation

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## Split Special Lagrangian Geometry

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 02/07/2010

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#Mathematics - Differential Geometry#Mathematics - Analysis of PDEs#Mathematics - Symplectic Geometry#Primary 53C42, Secondary 53C50, 35J96

One purpose of this article is to draw attention to the seminal work of J.
Mealy in 1989 on calibrations in semi-riemannian geometry where split SLAG
geometry was first introduced. The natural setting is provided by doing
geometry with the complex numbers C replaced by the double numbers D, where i
with i^2 = -1 is replaced by tau with tau^2 = 1. A rather surprising amount of
complex geometry carries over, almost untouched, and this has been the subject
of many papers. We briefly review this material and, in particular, we discuss
Hermitian D-manifolds with trivial canonical bundle, which provide the
background space for the geometry of split SLAG submanifolds.
A removable singularities result is proved for split SLAG subvarieties. It
implies, in particular, that there exist no split SLAG cones, smooth outside
the origin, other than planes. This is in sharp contrast to the complex case.
Parallel to the complex case, space-like Lagrangian submanifolds are
stationary if and only if they are theta-split SLAG for some phase angle theta,
and infinitesimal deformations of split SLAG submanifolds are characterized by
harmonic 1-forms on the submanifold.
We also briefly review the recent work of Kim, McCann and Warren who have
shown that split Special Lagrangian geometry is directly related to the
Monge-Kantorovich mass transport problem.

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## Strongly Homotopy Lie Algebras from Multisymplectic Geometry

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

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This Master Thesis is devoted to the study of $n$-plectic manifolds and the
Strongly Homotopy Lie algebras, also called $L_{\infty}$-algebras, that can be
associated to them. Since multisymplectic geometry and $L_{\infty}$-algebras
are relevant in Theoretical Physics, and in particular in String Theory, we
introduce the relevant background material in order to make the exposition
accessible to non-experts, perhaps interested physicists. The background
material includes graded and homological algebra theory, fibre bundles, basics
of group actions on manifolds and symplectic geometry. We give an introduction
to $L_{\infty}$-algebras and define $L_{\infty}$-morphisms in an independent
way, not yet related to multisymplectic geometry, giving explicit formulae
relating $L_{\infty}[1]$-algebras and $L_{\infty}$-algebras. We give also an
account of multisymplectic geometry and $n$-plectic manifolds, connecting them
to $L_{\infty}$-algebras. We then introduce, closely following the work
{1304.2051} of Yael Fregier, Christopher L. Rogers and Marco Zambon, the
concept of homotopy moment map. The new results presented here are the
following: we obtain specific conditions under which two $n$-plectic manifolds
with strictly isomorphic Lie-$n$ algebras are symplectomorphic...

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## Counting Algebraic Curves with Tropical Geometry

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 09/06/2012

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#Mathematics - Algebraic Geometry#Mathematics - Combinatorics#Primary: 14N35. Secondary: 14T05, 14N10

Tropical geometry is a piecewise linear "shadow" of algebraic geometry. It
allows for the computation of several cohomological invariants of an algebraic
variety. In particular, its application to enumerative algebraic geometry led
to significant progress.
In this survey, we give an introduction to tropical geometry techniques for
algebraic curve counting problems. We also survey some recent developments,
with a particular emphasis on the computation of the degree of the Severi
varieties of the complex projective plane and other toric surfaces as well as
Hurwitz numbers and applications to real enumerative geometry. This paper is
based on the author's lecture at the Workshop on Tropical Geometry and
Integrable Systems in Glasgow, July 2011.; Comment: 14 pages, 6 figures. To appear in Contemporary Mathematics
(Proceedings), "Tropical Geometry and Integrable Systems", Glasgow, July 2011

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## Nonholonomic Clifford Structures and Noncommutative Riemann--Finsler Geometry

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 09/08/2004

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#Mathematics - Differential Geometry#General Relativity and Quantum Cosmology#High Energy Physics - Theory#Mathematical Physics#46L87#51P05#53B20#53B40#70G45#83C65

We survey the geometry of Lagrange and Finsler spaces and discuss the issues
related to the definition of curvature of nonholonomic manifolds enabled with
nonlinear connection structure. It is proved that any commutative Riemannian
geometry (in general, any Riemann--Cartan space) defined by a generic
off--diagonal metric structure (with an additional affine connection possessing
nontrivial torsion) is equivalent to a generalized Lagrange, or Finsler,
geometry modeled on nonholonomic manifolds. This results in the problem of
constructing noncommutative geometries with local anisotropy, in particular,
related to geometrization of classical and quantum mechanical and field
theories, even if we restrict our considerations only to commutative and
noncommutative Riemannian spaces. We elaborate a geometric approach to the
Clifford modules adapted to nonlinear connections, to the theory of spinors and
the Dirac operators on nonholonomic spaces and consider possible
generalizations to noncommutative geometry. We argue that any commutative
Riemann--Finsler geometry and generalizations my be derived from
noncommutative geometry by applying certain methods elaborated for Riemannian
spaces but extended to nonholonomic frame transforms and manifolds provided
with nonlinear connection structure.; Comment: 55 pages...

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## Generalized complex geometry

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 18/01/2004

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Generalized complex geometry, as developed by Hitchin, contains complex and
symplectic geometry as its extremal special cases. In this thesis, we explore
novel phenomena exhibited by this geometry, such as the natural action of a
B-field. We provide new examples, including some on manifolds admitting no
known complex or symplectic structure. We prove a generalized Darboux theorem
which yields a local normal form for the geometry. We show that there is an
elliptic deformation theory and establish the existence of a Kuranishi moduli
space.
We then define the concept of a generalized Kahler manifold. We prove that
generalized Kahler geometry is equivalent to a bi-Hermitian geometry with
torsion first discovered by physicists. We then use this result to solve an
outstanding problem in 4-dimensional bi-Hermitian geometry: we prove that there
exists a Riemannian metric on the complex projective plane which admits exactly
two distinct Hermitian complex structures with equal orientation.
Finally, we introduce the concept of generalized complex submanifold, and
show that such sub-objects correspond to D-branes in the topological A- and
B-models of string theory.; Comment: Oxford University DPhil thesis, 107 pages

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## Mori geometry meets Cartan geometry: Varieties of minimal rational tangents

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 20/01/2015

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We give an introduction to the theory of varieties of minimal rational
tangents, emphasizing its aspect as a fusion of algebraic geometry and
differential geometry, more specifically, a fusion of Mori geometry of minimal
rational curves and Cartan geometry of cone structures.; Comment: to appear in Proceedings of ICM2014

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## tt* geometry, Frobenius manifolds, their connections, and the construction for singularities

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

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The base space of a semiuniversal unfolding of a hypersurface singularity
carries a rich geometry. By work of K. Saito and M. Saito is can be equipped
with the structure of a Frobenius manifold. By work of Cecotti and Vafa it can
be equipped with tt* geometry if the singularity is quasihomogeneous. tt*
geometry generalizes the notion of variation of Hodge structures.
In the second part of this paper (chapters 6-8) Frobenius manifolds and tt*
geometry are constructed for any hypersurface singularity, using essentially
oscillating integrals; and the intimate relationship between polarized mixed
Hodge structures and this tt* geometry is worked out.
In the first part (chapters 2-5) tt* geometry and Frobenius manifolds and
their relations are studied in general. To both of them flat connections with
poles are associated, with distinctive common and different properties. A frame
for a simultaneous construction is given.; Comment: 82 pages, amslatex, additional references, misprints corrected

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## D-branes and Azumaya/matrix noncommutative differential geometry, I: D-branes as fundamental objects in string theory and differentiable maps from Azumaya/matrix manifolds with a fundamental module to real manifolds

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 03/06/2014

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#Mathematics - Differential Geometry#High Energy Physics - Theory#Mathematics - Algebraic Geometry#Mathematics - Symplectic Geometry#58A40, 14A22, 81T30, 51K10, 16S50, 46L87

We consider D-branes in string theory and address the issue of how to
describe them mathematically as a fundamental object (as opposed to a solitonic
object) of string theory in the realm in differential and symplectic geometry.
The notion of continuous maps, $k$-times differentiable maps, and smooth maps
from an Azumaya/matrix manifold with a fundamental module to a (commutative)
real manifold $Y$ is developed. Such maps are meant to describe D-branes or
matrix branes in string theory when these branes are light and soft with only
small enough or even zero brane-tension. When $Y$ is a symplectic manifold
(resp. a Calabi-Yau manifold; a $7$-manifold with $G_2$-holonomy; a manifold
with an almost complex structure $J$), the corresponding notion of Lagrangian
maps (resp. special Lagrangian maps; associative maps, coassociative maps;
$J$-holomorphic maps) are introduced. Indicative examples linking to symplectic
geometry and string theory are given. This provides us with a language and part
of the foundation required to study themes, new or old, in symplectic geometry
and string theory, including (1) $J$-holomorphic D-curves (with or without
boundary), (2) quantization and dynamics of D-branes in string theory, (3) a
definition of Fukaya category guided by Lagrangian maps from Azumaya manifolds
with a fundamental module with a connection...

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## Influence of the subducting plate velocity on the geometry of the slab and migration of the subduction hinge

Fonte: Elsevier
Publicador: Elsevier

Tipo: Artigo de Revista Científica

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#Keywords: Back-arc opening#Hinge-retreat#Plate velocity#Slab geometry#Computer simulation#Fluid dynamics#Geometry#Hinges#Kinematics#Vectors#Velocity measurement

Geological observations indicate that along two active continental margins (East Asia and Mediterranean) major phases of overriding plate extension, resulting from subduction hinge-retreat, occurred synchronously with a reduction in subducting plate velocity. In this paper, results of fluid dynamical experiments are presented to test the influence of the velocity of the subducting plate on the hinge-migration velocity and on the geometry of the slab. Results show that hinge-retreat decreases with increasing subducting plate velocity. In addition, phases of hinge-retreat alternate with phases of hinge-advance for relatively high subducting plate velocities due to interaction of the slab with the bottom of the box, simulating the upper-lower mantle discontinuity. Such slab kinematics could explain the episodic behaviour of back-arc opening observed in convergent settings. The geometry of the slab and the kinematics of subduction are significantly affected by the velocity of the subducting plate. Three subduction modes with accompanying slab geometry can be recognized. A relatively low subducting plate velocity is accompanied by relatively fast hinge-retreat with backward sinking of the slab and a backward draping slab geometry. With increasing subducting plate velocity hinge-migration is relatively small...

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