Handbook Of Pseudo Riemannian Geometry And Supersymmetry

Author : Vicente Cortés
Publisher : European Mathematical Society
Page : 972 pages
File Size : 54,6 Mb
Release : 2010
Category : Geometry, Riemannian
ISBN : 3037190795

Get Book

Handbook of Pseudo-Riemannian Geometry and Supersymmetry by Vicente Cortés Pdf

The purpose of this handbook is to give an overview of some recent developments in differential geometry related to supersymmetric field theories. The main themes covered are: Special geometry and supersymmetry Generalized geometry Geometries with torsion Para-geometries Holonomy theory Symmetric spaces and spaces of constant curvature Conformal geometry Wave equations on Lorentzian manifolds D-branes and K-theory The intended audience consists of advanced students and researchers working in differential geometry, string theory, and related areas. The emphasis is on geometrical structures occurring on target spaces of supersymmetric field theories. Some of these structures can be fully described in the classical framework of pseudo-Riemannian geometry. Others lead to new concepts relating various fields of research, such as special Kahler geometry or generalized geometry.

Author : VICENTE CORTES.
Publisher : Unknown
Page : 128 pages
File Size : 49,7 Mb
Release : 2024-06-06
Category : Electronic
ISBN : 3037195797

Get Book

HANDBOOK OF PSEUDO-RIEMANNIAN GEOMETRY AND SUPERSYMMETRY. by VICENTE CORTES. Pdf

Author : Dmitriĭ Vladimirovich Alekseevskiĭ
Publisher : European Mathematical Society
Page : 556 pages
File Size : 51,6 Mb
Release : 2008
Category : Mathematics
ISBN : 3037190515

Get Book

Recent Developments in Pseudo-Riemannian Geometry by Dmitriĭ Vladimirovich Alekseevskiĭ Pdf

This book provides an introduction to and survey of recent developments in pseudo-Riemannian geometry, including applications in mathematical physics, by leading experts in the field. Topics covered are: Classification of pseudo-Riemannian symmetric spaces Holonomy groups of Lorentzian and pseudo-Riemannian manifolds Hypersymplectic manifolds Anti-self-dual conformal structures in neutral signature and integrable systems Neutral Kahler surfaces and geometric optics Geometry and dynamics of the Einstein universe Essential conformal structures and conformal transformations in pseudo-Riemannian geometry The causal hierarchy of spacetimes Geodesics in pseudo-Riemannian manifolds Lorentzian symmetric spaces in supergravity Generalized geometries in supergravity Einstein metrics with Killing leaves The book is addressed to advanced students as well as to researchers in differential geometry, global analysis, general relativity and string theory. It shows essential differences between the geometry on manifolds with positive definite metrics and on those with indefinite metrics, and highlights the interesting new geometric phenomena, which naturally arise in the indefinite metric case. The reader finds a description of the present state of the art in the field as well as open problems, which can stimulate further research.

Author : Luis Carlos de Andrés
Publisher : American Institute of Physics
Page : 220 pages
File Size : 48,9 Mb
Release : 2009-02-25
Category : Mathematics
ISBN : UCSD:31822036973691

Get Book

Special Metrics and Supersymmetry by Luis Carlos de Andrés Pdf

All papers have been peer-reviewed. This volume includes the contributions to the International Workshop on Geometry and Physics: Special Metrics and Supersymmetry, held at the University of the Basque Country, Bilbao (Spain), from May 29 to 31, 2008. The topics covered by the volume deal with leading aspects of algebraic and differential geometry with special emphasis to their potential applications in supersymmetry and string theories. The areas covered by the proceedings are algebraic geometry, differential geometry and mathematical physics. In greater detail, they cover outstanding topics such as homological mirror symmetry, generalized Hodge theory, coassociative submanifolds, special geometric structures, geometric structures, Killing spinors, torsion geometry, string theory, supersymmetry and T-duality, among others.

Author : Peter B. Gilkey
Publisher : World Scientific
Page : 389 pages
File Size : 45,9 Mb
Release : 2007
Category : Science
ISBN : 9781860947858

Get Book

The Geometry of Curvature Homogeneous Pseudo-Riemannian Manifolds by Peter B. Gilkey Pdf

"Pseudo-Riemannian geometry is an active research field not only in differential geometry but also in mathematical physics where the higher signature geometries play a role in brane theory. An essential reference tool for research mathematicians and physicists, this book also serves as a useful introduction to students entering this active and rapidly growing field. The author presents a comprehensive treatment of several aspects of pseudo-Riemannian geometry, including the spectral geometry of the curvature tensor, curvature homogeneity, and Stanilov-Tsankov-Videv theory."--BOOK JACKET.

Author : Lars Schäfer
Publisher : Springer
Page : 183 pages
File Size : 50,6 Mb
Release : 2017-09-14
Category : Mathematics
ISBN : 9783319658070

Get Book

Nearly Pseudo-Kähler Manifolds and Related Special Holonomies by Lars Schäfer Pdf

Developing and providing an overview of recent results on nearly Kähler geometry on pseudo-Riemannian manifolds, this monograph emphasizes the differences with the classical Riemannian geometry setting. The focal objects of the text are related to special holonomy and Killing spinors and have applications in high energy physics, such as supergravity and string theory. Before starting into the field, a self-contained introduction to the subject is given, aimed at students with a solid background in differential geometry. The book will therefore be accessible to masters and Ph.D. students who are beginning work on nearly Kähler geometry in pseudo-Riemannian signature, and also to non-experts interested in gaining an overview of the subject. Moreover, a number of results and techniques are provided which will be helpful for differential geometers as well as for high energy physicists interested in the mathematical background of the geometric objects they need.

Author : Sorin Dragomir,Mohammad Hasan Shahid,Falleh R. Al-Solamy
Publisher : Springer
Page : 390 pages
File Size : 51,6 Mb
Release : 2016-05-31
Category : Mathematics
ISBN : 9789811009167

Get Book

Geometry of Cauchy-Riemann Submanifolds by Sorin Dragomir,Mohammad Hasan Shahid,Falleh R. Al-Solamy Pdf

This book gathers contributions by respected experts on the theory of isometric immersions between Riemannian manifolds, and focuses on the geometry of CR structures on submanifolds in Hermitian manifolds. CR structures are a bundle theoretic recast of the tangential Cauchy–Riemann equations in complex analysis involving several complex variables. The book covers a wide range of topics such as Sasakian geometry, Kaehler and locally conformal Kaehler geometry, the tangential CR equations, Lorentzian geometry, holomorphic statistical manifolds, and paraquaternionic CR submanifolds. Intended as a tribute to Professor Aurel Bejancu, who discovered the notion of a CR submanifold of a Hermitian manifold in 1978, the book provides an up-to-date overview of several topics in the geometry of CR submanifolds. Presenting detailed information on the most recent advances in the area, it represents a useful resource for mathematicians and physicists alike.

Author : Athanase Papadopoulos
Publisher : European Mathematical Society
Page : 876 pages
File Size : 41,6 Mb
Release : 2007
Category : Teichm uller spaces
ISBN : 3037191031

Get Book

Handbook of Teichmüller Theory by Athanase Papadopoulos Pdf

The subject of this handbook is Teichmuller theory in a wide sense, namely the theory of geometric structures on surfaces and their moduli spaces. This includes the study of vector bundles on these moduli spaces, the study of mapping class groups, the relation with $3$-manifolds, the relation with symmetric spaces and arithmetic groups, the representation theory of fundamental groups, and applications to physics. Thus the handbook is a place where several fields of mathematics interact: Riemann surfaces, hyperbolic geometry, partial differential equations, several complex variables, algebraic geometry, algebraic topology, combinatorial topology, low-dimensional topology, theoretical physics, and others. This confluence of ideas toward a unique subject is a manifestation of the unity and harmony of mathematics. This volume contains surveys on the fundamental theory as well as surveys on applications to and relations with the fields mentioned above. It is written by leading experts in these fields. Some of the surveys contain classical material, while others present the latest developments of the theory as well as open problems. This volume is divided into the following four sections: The metric and the analytic theory The group theory The algebraic topology of mapping class groups and moduli spaces Teichmuller theory and mathematical physics This handbook is addressed to graduate students and researchers in all the fields mentioned.

Author : Giovanni Calvaruso,Marco Castrillón López
Publisher : Springer
Page : 230 pages
File Size : 54,5 Mb
Release : 2019-08-14
Category : Mathematics
ISBN : 9783030181529

Get Book

Pseudo-Riemannian Homogeneous Structures by Giovanni Calvaruso,Marco Castrillón López Pdf

This book provides an up-to-date presentation of homogeneous pseudo-Riemannian structures, an essential tool in the study of pseudo-Riemannian homogeneous spaces. Benefiting from large symmetry groups, these spaces are of high interest in Geometry and Theoretical Physics. Since the seminal book by Tricerri and Vanhecke, the theory of homogeneous structures has been considerably developed and many applications have been found. The present work covers a gap in the literature of more than 35 years, presenting the latest contributions to the field in a modern geometric approach, with special focus on manifolds equipped with pseudo-Riemannian metrics. This unique reference on the topic will be of interest to researchers working in areas of mathematics where homogeneous spaces play an important role, such as Differential Geometry, Global Analysis, General Relativity, and Particle Physics.

Author : Krzysztof Galicki,Santiago R. Simanca
Publisher : Springer Science & Business Media
Page : 290 pages
File Size : 47,9 Mb
Release : 2010-07-25
Category : Mathematics
ISBN : 9780817647438

Get Book

Riemannian Topology and Geometric Structures on Manifolds by Krzysztof Galicki,Santiago R. Simanca Pdf

Riemannian Topology and Structures on Manifolds results from a similarly entitled conference held on the occasion of Charles P. Boyer’s 65th birthday. The various contributions to this volume discuss recent advances in the areas of positive sectional curvature, Kähler and Sasakian geometry, and their interrelation to mathematical physics, especially M and superstring theory. Focusing on these fundamental ideas, this collection presents review articles, original results, and open problems of interest.

Author : Edoardo Lauria,Antoine Van Proeyen
Publisher : Springer Nature
Page : 265 pages
File Size : 50,5 Mb
Release : 2020-03-11
Category : Science
ISBN : 9783030337575

Get Book

N = 2 Supergravity in D = 4, 5, 6 Dimensions by Edoardo Lauria,Antoine Van Proeyen Pdf

This graduate-level primer presents a tutorial introduction to and overview of N = 2 supergravity theories - with 8 real supercharges and in 4, 5 and 6 dimensions. First, the construction of such theories by superconformal methods is explained in detail, and relevant special geometries are obtained and characterized. Following, the relation between the supergravity theories in the various dimensions is discussed. This leads eventually to the concept of very special geometry and quaternionic-Kähler manifolds. This concise text is a valuable resource for graduate students and young researchers wishing to enter the field quickly and efficiently.

Author : Athanase Papadopoulos
Publisher : European Mathematical Society
Page : 468 pages
File Size : 50,7 Mb
Release : 2012
Category : Geometry
ISBN : 3037191058

Get Book

Strasbourg Master Class on Geometry by Athanase Papadopoulos Pdf

This book contains carefully revised and expanded versions of eight courses that were presented at the University of Strasbourg during two geometry master classes in 2008 and 2009. The aim of the master classes was to give fifth-year students and Ph.D. students in mathematics the opportunity to learn new topics that lead directly to the current research in geometry and topology. The courses were taught by leading experts. The subjects treated include hyperbolic geometry, three-manifold topology, representation theory of fundamental groups of surfaces and of three-manifolds, dynamics on the hyperbolic plane with applications to number theory, Riemann surfaces, Teichmuller theory, Lie groups, and asymptotic geometry. The text is aimed at graduate students and research mathematicians. It can also be used as a reference book and as a textbook for short courses on geometry.

Author : Bogdan D. Suceavă,Alfonso Carriazo,Yun Myung Oh,Joeri Van der Veken
Publisher : American Mathematical Soc.
Page : 209 pages
File Size : 44,5 Mb
Release : 2016-09-14
Category : Differential geometry -- Local differential geometry -- Local submanifolds
ISBN : 9781470422981

Get Book

Recent Advances in the Geometry of Submanifolds by Bogdan D. Suceavă,Alfonso Carriazo,Yun Myung Oh,Joeri Van der Veken Pdf

This volume contains the proceedings of the AMS Special Session on Geometry of Submanifolds, held from October 25–26, 2014, at San Francisco State University, San Francisco, CA, and the AMS Special Session on Recent Advances in the Geometry of Submanifolds: Dedicated to the Memory of Franki Dillen (1963–2013), held from March 14–15, 2015, at Michigan State University, East Lansing, Ml. The focus of the volume is on recent studies of submanifolds of Riemannian, semi-Riemannian, Kaehlerian and contact manifolds. Some of these use techniques in classical differential geometry, while others use methods from ordinary differential equations, geometric analysis, or geometric PDEs. By brainstorming on the fundamental problems and exploring a large variety of questions studied in submanifold geometry, the editors hope to provide mathematicians with a working tool, not just a collection of individual contributions. This volume is dedicated to the memory of Franki Dillen, whose work in submanifold theory attracted the attention of and inspired many geometers.

Author : Xianzhe Dai,Xiaochun Rong
Publisher : Springer Science & Business Media
Page : 364 pages
File Size : 53,8 Mb
Release : 2012-06-01
Category : Mathematics
ISBN : 9783034802574

Get Book

Metric and Differential Geometry by Xianzhe Dai,Xiaochun Rong Pdf

Metric and Differential Geometry grew out of a similarly named conference held at Chern Institute of Mathematics, Tianjin and Capital Normal University, Beijing. The various contributions to this volume cover a broad range of topics in metric and differential geometry, including metric spaces, Ricci flow, Einstein manifolds, Kähler geometry, index theory, hypoelliptic Laplacian and analytic torsion. It offers the most recent advances as well as surveys the new developments. Contributors: M.T. Anderson J.-M. Bismut X. Chen X. Dai R. Harvey P. Koskela B. Lawson X. Ma R. Melrose W. Müller A. Naor J. Simons C. Sormani D. Sullivan S. Sun G. Tian K. Wildrick W. Zhang

Author : Eberhard Zeidler
Publisher : Springer Science & Business Media
Page : 1141 pages
File Size : 42,8 Mb
Release : 2011-08-17
Category : Mathematics
ISBN : 9783642224218

Get Book

Quantum Field Theory III: Gauge Theory by Eberhard Zeidler Pdf

In this third volume of his modern introduction to quantum field theory, Eberhard Zeidler examines the mathematical and physical aspects of gauge theory as a principle tool for describing the four fundamental forces which act in the universe: gravitative, electromagnetic, weak interaction and strong interaction. Volume III concentrates on the classical aspects of gauge theory, describing the four fundamental forces by the curvature of appropriate fiber bundles. This must be supplemented by the crucial, but elusive quantization procedure. The book is arranged in four sections, devoted to realizing the universal principle force equals curvature: Part I: The Euclidean Manifold as a Paradigm Part II: Ariadne's Thread in Gauge Theory Part III: Einstein's Theory of Special Relativity Part IV: Ariadne's Thread in Cohomology For students of mathematics the book is designed to demonstrate that detailed knowledge of the physical background helps to reveal interesting interrelationships among diverse mathematical topics. Physics students will be exposed to a fairly advanced mathematics, beyond the level covered in the typical physics curriculum. Quantum Field Theory builds a bridge between mathematicians and physicists, based on challenging questions about the fundamental forces in the universe (macrocosmos), and in the world of elementary particles (microcosmos).