Homogeneous Structures On Riemannian Manifolds
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Homogeneous Structures On Riemannian Manifolds
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Author : F. Tricerri
language : en
Publisher: Cambridge University Press
Release Date : 1983-06-23
Homogeneous Structures On Riemannian Manifolds written by F. Tricerri and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1983-06-23 with Mathematics categories.
The central theme of this book is the theorem of Ambrose and Singer, which gives for a connected, complete and simply connected Riemannian manifold a necessary and sufficient condition for it to be homogeneous. This is a local condition which has to be satisfied at all points, and in this way it is a generalization of E. Cartan's method for symmetric spaces. The main aim of the authors is to use this theorem and representation theory to give a classification of homogeneous Riemannian structures on a manifold. There are eight classes, and some of these are discussed in detail. Using the constructive proof of Ambrose and Singer many examples are discussed with special attention to the natural correspondence between the homogeneous structure and the groups acting transitively and effectively as isometrics on the manifold.
Homogeneous Structures On Riemannian Manifolds
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Author : Franco Tricerri
language : en
Publisher:
Release Date : 2014-05-14
Homogeneous Structures On Riemannian Manifolds written by Franco Tricerri and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-14 with MATHEMATICS categories.
The central theme of this book is the theorem of Ambrose and Singer, which gives for a connected, complete and simply connected Riemannian manifold a necessary and sufficient condition for it to be homogeneous. This is a local condition which has to be satisfied at all points, and in this way it is a generalization of E. Cartan's method for symmetric spaces. The main aim of the authors is to use this theorem and representation theory to give a classification of homogeneous Riemannian structures on a manifold. There are eight classes, and some of these are discussed in detail. Using the constructive proof of Ambrose and Singer many examples are discussed with special attention to the natural correspondence between the homogeneous structure and the groups acting transitively and effectively as isometrics on the manifold.
Homogeneous Structures On Riemannian Manifolds
DOWNLOAD
Author : F. Tricerri
language : en
Publisher: Cambridge University Press
Release Date : 1983-06-23
Homogeneous Structures On Riemannian Manifolds written by F. Tricerri and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1983-06-23 with Mathematics categories.
The central theme of this book is the theorem of Ambrose and Singer, which gives for a connected, complete and simply connected Riemannian manifold a necessary and sufficient condition for it to be homogeneous. This is a local condition which has to be satisfied at all points, and in this way it is a generalization of E. Cartan's method for symmetric spaces. The main aim of the authors is to use this theorem and representation theory to give a classification of homogeneous Riemannian structures on a manifold. There are eight classes, and some of these are discussed in detail. Using the constructive proof of Ambrose and Singer many examples are discussed with special attention to the natural correspondence between the homogeneous structure and the groups acting transitively and effectively as isometrics on the manifold.
Pseudo Riemannian Homogeneous Structures
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Author : Giovanni Calvaruso
language : en
Publisher: Springer
Release Date : 2019-08-14
Pseudo Riemannian Homogeneous Structures written by Giovanni Calvaruso and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-08-14 with Mathematics categories.
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.
The Volume Of Vector Fields On Riemannian Manifolds
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Author : Olga Gil-Medrano
language : en
Publisher: Springer Nature
Release Date : 2023-07-31
The Volume Of Vector Fields On Riemannian Manifolds written by Olga Gil-Medrano and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-07-31 with Mathematics categories.
This book focuses on the study of the volume of vector fields on Riemannian manifolds. Providing a thorough overview of research on vector fields defining minimal submanifolds, and on the existence and characterization of volume minimizers, it includes proofs of the most significant results obtained since the subject’s introduction in 1986. Aiming to inspire further research, it also highlights a selection of intriguing open problems, and exhibits some previously unpublished results. The presentation is direct and deviates substantially from the usual approaches found in the literature, requiring a significant revision of definitions, statements, and proofs. A wide range of topics is covered, including: a discussion on the conditions for a vector field on a Riemannian manifold to determine a minimal submanifold within its tangent bundle with the Sasaki metric; numerous examples of minimal vector fields (including those of constant length on punctured spheres); a thorough analysis of Hopf vector fields on odd-dimensional spheres and their quotients; and a description of volume-minimizing vector fields of constant length on spherical space forms of dimension three. Each chapter concludes with an up-to-date survey which offers supplementary information and provides valuable insights into the material, enhancing the reader's understanding of the subject. Requiring a solid understanding of the fundamental concepts of Riemannian geometry, the book will be useful for researchers and PhD students with an interest in geometric analysis.
Complex Analysis And Geometry
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Author : Vincenzo Ancona
language : en
Publisher: CRC Press
Release Date : 1997-04-27
Complex Analysis And Geometry written by Vincenzo Ancona and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-04-27 with Mathematics categories.
Based on two conferences held in Trento, Italy, this volume contains 13 research papers and two survey papers on complex analysis and complex algebraic geometry. The main topics addressed by these leading researchers include: Mori theory polynomial hull vector bundles q-convexity Lie groups and actions on complex spaces hypercomplex structures pseudoconvex domains projective varieties Peer-reviewed and extensively referenced, Complex Analysis and Geometry contains recent advances and important research results. It also details several problems that remain open, the resolution of which could further advance the field.
The Geometry Of Walker Manifolds
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Author : Peter Gilkey
language : en
Publisher: Springer Nature
Release Date : 2022-05-31
The Geometry Of Walker Manifolds written by Peter Gilkey and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-05-31 with Mathematics categories.
This book, which focuses on the study of curvature, is an introduction to various aspects of pseudo-Riemannian geometry. We shall use Walker manifolds (pseudo-Riemannian manifolds which admit a non-trivial parallel null plane field) to exemplify some of the main differences between the geometry of Riemannian manifolds and the geometry of pseudo-Riemannian manifolds and thereby illustrate phenomena in pseudo-Riemannian geometry that are quite different from those which occur in Riemannian geometry, i.e. for indefinite as opposed to positive definite metrics. Indefinite metrics are important in many diverse physical contexts: classical cosmological models (general relativity) and string theory to name but two. Walker manifolds appear naturally in numerous physical settings and provide examples of extremal mathematical situations as will be discussed presently. To describe the geometry of a pseudo-Riemannian manifold, one must first understand the curvature of the manifold. We shall analyze a wide variety of curvature properties and we shall derive both geometrical and topological results. Special attention will be paid to manifolds of dimension 3 as these are quite tractable. We then pass to the 4 dimensional setting as a gateway to higher dimensions. Since the book is aimed at a very general audience (and in particular to an advanced undergraduate or to a beginning graduate student), no more than a basic course in differential geometry is required in the way of background. To keep our treatment as self-contained as possible, we shall begin with two elementary chapters that provide an introduction to basic aspects of pseudo-Riemannian geometry before beginning on our study of Walker geometry. An extensive bibliography is provided for further reading. Math subject classifications : Primary: 53B20 -- (PACS: 02.40.Hw) Secondary: 32Q15, 51F25, 51P05, 53B30, 53C50, 53C80, 58A30, 83F05, 85A04 Table of Contents: Basic Algebraic Notions / Basic Geometrical Notions / Walker Structures / Three-Dimensional Lorentzian Walker Manifolds / Four-Dimensional Walker Manifolds / The Spectral Geometry of the Curvature Tensor / Hermitian Geometry / Special Walker Manifolds
Geometry Algebra And Applications From Mechanics To Cryptography
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Author : Marco Castrillón López
language : en
Publisher: Springer
Release Date : 2016-06-30
Geometry Algebra And Applications From Mechanics To Cryptography written by Marco Castrillón López and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-06-30 with Science categories.
This volume collects contributions written by different experts in honor of Prof. Jaime Muñoz Masqué. It covers a wide variety of research topics, from differential geometry to algebra, but particularly focuses on the geometric formulation of variational calculus; geometric mechanics and field theories; symmetries and conservation laws of differential equations, and pseudo-Riemannian geometry of homogeneous spaces. It also discusses algebraic applications to cryptography and number theory. It offers state-of-the-art contributions in the context of current research trends. The final result is a challenging panoramic view of connecting problems that initially appear distant.
Riemannian Manifolds Of Conullity Two
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Author : Eric Boeckx
language : en
Publisher: World Scientific
Release Date : 1996-11-09
Riemannian Manifolds Of Conullity Two written by Eric Boeckx and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-11-09 with Mathematics categories.
This book deals with Riemannian manifolds for which the nullity space of the curvature tensor has codimension two. These manifolds are “semi-symmetric spaces foliated by Euclidean leaves of codimension two” in the sense of Z I Szabó. The authors concentrate on the rich geometrical structure and explicit descriptions of these remarkable spaces. Also parallel theories are developed for manifolds of “relative conullity two”. This makes a bridge to a survey on curvature homogeneous spaces introduced by I M Singer. As an application of the main topic, interesting hypersurfaces with type number two in Euclidean space are discovered, namely those which are locally rigid or “almost rigid”. The unifying method is solving explicitly particular systems of nonlinear PDE.
Riemannian Submersions And Related Topics
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Author : Anna Maria Pastore
language : en
Publisher: World Scientific
Release Date : 2004-06-21
Riemannian Submersions And Related Topics written by Anna Maria Pastore and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-06-21 with Mathematics categories.
This book provides the first-ever systematic introduction to the theory of Riemannian submersions, which was initiated by Barrett O'Neill and Alfred Gray less than four decades ago. The authors focus their attention on classification theorems when the total space and the fibres have nice geometric properties. Particular emphasis is placed on the interrelation with almost Hermitian, almost contact and quaternionic geometry. Examples clarifying and motivating the theory are included in every chapter. Recent results on semi-Riemannian submersions are also explained. Finally, the authors point out the close connection of the subject with some areas of physics.