Classification Theory Of Riemannian Manifolds
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Classification Theory Of Riemannian Manifolds
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Author : S. R. Sario
language : en
Publisher:
Release Date : 2014-01-15
Classification Theory Of Riemannian Manifolds written by S. R. Sario and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.
Classification Theory Of Riemannian Manifolds
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Author : S. R. Sario
language : en
Publisher: Springer
Release Date : 2006-11-15
Classification Theory Of Riemannian Manifolds written by S. R. Sario and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.
Classification Theory Of Riemann Surfaces
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Author : Leo Sario
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Classification Theory Of Riemann Surfaces written by Leo Sario and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
The purpose of the present monograph is to systematically develop a classification theory of Riemann surfaces. Some first steps will also be taken toward a classification of Riemannian spaces. Four phases can be distinguished in the chronological background: the type problem; general classification; compactifications; and extension to higher dimensions. The type problem evolved in the following somewhat overlapping steps: the Riemann mapping theorem, the classical type problem, and the existence of Green's functions. The Riemann mapping theorem laid the foundation to classification theory: there are only two conformal equivalence classes of (noncompact) simply connected regions. Over half a century of efforts by leading mathematicians went into giving a rigorous proof of the theorem: RIEMANN, WEIERSTRASS, SCHWARZ, NEUMANN, POINCARE, HILBERT, WEYL, COURANT, OSGOOD, KOEBE, CARATHEODORY, MONTEL. The classical type problem was to determine whether a given simply connected covering surface of the plane is conformally equivalent to the plane or the disko The problem was in the center of interest in the thirties and early forties, with AHLFORS, KAKUTANI, KOBAYASHI, P. MYRBERG, NEVANLINNA, SPEISER, TEICHMÜLLER and others obtaining incisive specific results. The main problem of finding necessary and sufficient conditions remains, however, unsolved.
The Laplacian On A Riemannian Manifold
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Author : Steven Rosenberg
language : en
Publisher: Cambridge University Press
Release Date : 1997-01-09
The Laplacian On A Riemannian Manifold written by Steven Rosenberg 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 1997-01-09 with Mathematics categories.
This text on analysis of Riemannian manifolds is aimed at students who have had a first course in differentiable manifolds.
Manifolds Ii
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Author : Paul Bracken
language : en
Publisher: BoD – Books on Demand
Release Date : 2019-05-22
Manifolds Ii written by Paul Bracken and has been published by BoD – Books on Demand this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-05-22 with Mathematics categories.
Differential geometry is a very active field of research and has many applications to areas such as physics, in particular gravity. The chapters in this book cover a number of subjects that will be of interest to workers in these areas. It is hoped that these chapters will be able to provide a useful resource for researchers with regard to current fields of research in this important area.
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.
Nonlinear Potential Theory And Quasiregular Mappings On Riemannian Manifolds
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Author : Ilkka Holopainen
language : en
Publisher:
Release Date : 1990
Nonlinear Potential Theory And Quasiregular Mappings On Riemannian Manifolds written by Ilkka Holopainen and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with Harmonic maps categories.
Recent Developments In Pseudo Riemannian Geometry
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Author : Dmitriĭ Vladimirovich Alekseevskiĭ
language : en
Publisher: European Mathematical Society
Release Date : 2008
Recent Developments In Pseudo Riemannian Geometry written by Dmitriĭ Vladimirovich Alekseevskiĭ and has been published by European Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.
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.
Coarse Cohomology And Index Theory On Complete Riemannian Manifolds
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Author : John Roe
language : en
Publisher: American Mathematical Soc.
Release Date : 1993
Coarse Cohomology And Index Theory On Complete Riemannian Manifolds written by John Roe and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with Mathematics categories.
"July 1993, volume 104, number 497 (fourth of 6 numbers)."
Twistor Theory For Riemannian Symmetric Spaces
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Author : Francis E. Burstall
language : en
Publisher: Springer
Release Date : 2006-11-14
Twistor Theory For Riemannian Symmetric Spaces written by Francis E. Burstall and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.
In this monograph on twistor theory and its applications to harmonic map theory, a central theme is the interplay between the complex homogeneous geometry of flag manifolds and the real homogeneous geometry of symmetric spaces. In particular, flag manifolds are shown to arise as twistor spaces of Riemannian symmetric spaces. Applications of this theory include a complete classification of stable harmonic 2-spheres in Riemannian symmetric spaces and a Bäcklund transform for harmonic 2-spheres in Lie groups which, in many cases, provides a factorisation theorem for such spheres as well as gap phenomena. The main methods used are those of homogeneous geometry and Lie theory together with some algebraic geometry of Riemann surfaces. The work addresses differential geometers, especially those with interests in minimal surfaces and homogeneous manifolds.