Spaces Of Constant Curvature
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Spaces Of Constant Curvature
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Author : Joseph Albert Wolf
language : en
Publisher: American Mathematical Soc.
Release Date : 2011
Spaces Of Constant Curvature written by Joseph Albert Wolf 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 2011 with Mathematics categories.
This book is the sixth edition of the classic Spaces of Constant Curvature, first published in 1967, with the previous (fifth) edition published in 1984. It illustrates the high degree of interplay between group theory and geometry. The reader will benefit from the very concise treatments of riemannian and pseudo-riemannian manifolds and their curvatures, of the representation theory of finite groups, and of indications of recent progress in discrete subgroups of Lie groups. Part I is a brief introduction to differentiable manifolds, covering spaces, and riemannian and pseudo-riemannian geometry. It also contains a certain amount of introductory material on symmetry groups and space forms, indicating the direction of the later chapters. Part II is an updated treatment of euclidean space form. Part III is Wolf's classic solution to the Clifford-Klein Spherical Space Form Problem. It starts with an exposition of the representation theory of finite groups. Part IV introduces riemannian symmetric spaces and extends considerations of spherical space forms to space forms of riemannian symmetric spaces. Finally, Part V examines space form problems on pseudo-riemannian symmetric spaces. At the end of Chapter 12 there is a new appendix describing some of the recent work on discrete subgroups of Lie groups with application to space forms of pseudo-riemannian symmetric spaces. Additional references have been added to this sixth edition as well.
Spaces Of Constant Curvature
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Author : Joseph A. Wolf
language : en
Publisher: American Mathematical Society
Release Date : 2023-06-05
Spaces Of Constant Curvature written by Joseph A. Wolf and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-06-05 with Mathematics categories.
This book is the sixth edition of the classic Spaces of Constant Curvature, first published in 1967, with the previous (fifth) edition published in 1984. It illustrates the high degree of interplay between group theory and geometry. The reader will benefit from the very concise treatments of riemannian and pseudo-riemannian manifolds and their curvatures, of the representation theory of finite groups, and of indications of recent progress in discrete subgroups of Lie groups. Part I is a brief introduction to differentiable manifolds, covering spaces, and riemannian and pseudo-riemannian geometry. It also contains a certain amount of introductory material on symmetry groups and space forms, indicating the direction of the later chapters. Part II is an updated treatment of euclidean space form. Part III is Wolf's classic solution to the Clifford–Klein Spherical Space Form Problem. It starts with an exposition of the representation theory of finite groups. Part IV introduces riemannian symmetric spaces and extends considerations of spherical space forms to space forms of riemannian symmetric spaces. Finally, Part V examines space form problems on pseudo-riemannian symmetric spaces. At the end of Chapter 12 there is a new appendix describing some of the recent work on discrete subgroups of Lie groups with application to space forms of pseudo-riemannian symmetric spaces. Additional references have been added to this sixth edition as well.
Geometry Ii
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Author : E.B. Vinberg
language : en
Publisher: Springer
Release Date : 2014-03-12
Geometry Ii written by E.B. Vinberg and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-03-12 with Mathematics categories.
A very clear account of the subject from the viewpoints of elementary geometry, Riemannian geometry and group theory – a book with no rival in the literature. Mostly accessible to first-year students in mathematics, the book also includes very recent results which will be of interest to researchers in this field.
Geometry Ii
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Author : E.B. Vinberg
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
Geometry Ii written by E.B. Vinberg 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 2013-04-17 with Mathematics categories.
A very clear account of the subject from the viewpoints of elementary geometry, Riemannian geometry and group theory – a book with no rival in the literature. Mostly accessible to first-year students in mathematics, the book also includes very recent results which will be of interest to researchers in this field.
Ii Geometry
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Author :
language : en
Publisher:
Release Date : 1993
Ii Geometry written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with Geometry categories.
中国科学院科学出版基金资助出版
Quantum Mechanics In Spaces Of Constant Curvature
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Author : V. M. Redkov
language : en
Publisher:
Release Date : 2012
Quantum Mechanics In Spaces Of Constant Curvature written by V. M. Redkov and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Quantum theory categories.
Includes bibliographical references (p. [401]-429) and index.
Spaces Of Constant Curvature
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Author : Joseph Albert Wolf
language : en
Publisher:
Release Date : 1974
Spaces Of Constant Curvature written by Joseph Albert Wolf and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1974 with Mathematics categories.
Separation Of Variables For Riemannian Spaces Of Constant Curvature
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Author : E. G. Kalnins
language : en
Publisher: Longman Scientific and Technical
Release Date : 1986
Separation Of Variables For Riemannian Spaces Of Constant Curvature written by E. G. Kalnins and has been published by Longman Scientific and Technical this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986 with Mathematics categories.
Comprehensive and up-to-date survey of research on torsion theories defined on module categories over noncommutative rings and the use in the localization of rings and modules.
Integrable Problems Of Celestial Mechanics In Spaces Of Constant Curvature
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Author : T.G. Vozmischeva
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
Integrable Problems Of Celestial Mechanics In Spaces Of Constant Curvature written by T.G. Vozmischeva 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 2013-04-17 with Science categories.
Introd uction The problem of integrability or nonintegrability of dynamical systems is one of the central problems of mathematics and mechanics. Integrable cases are of considerable interest, since, by examining them, one can study general laws of behavior for the solutions of these systems. The classical approach to studying dynamical systems assumes a search for explicit formulas for the solutions of motion equations and then their analysis. This approach stimulated the development of new areas in mathematics, such as the al gebraic integration and the theory of elliptic and theta functions. In spite of this, the qualitative methods of studying dynamical systems are much actual. It was Poincare who founded the qualitative theory of differential equa tions. Poincare, working out qualitative methods, studied the problems of celestial mechanics and cosmology in which it is especially important to understand the behavior of trajectories of motion, i.e., the solutions of differential equations at infinite time. Namely, beginning from Poincare systems of equations (in connection with the study of the problems of ce lestial mechanics), the right-hand parts of which don't depend explicitly on the independent variable of time, i.e., dynamical systems, are studied.
Quantum Mechanics In Spaces Of Constant Curvature
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Author : V. M. Redkov
language : en
Publisher:
Release Date : 2012
Quantum Mechanics In Spaces Of Constant Curvature written by V. M. Redkov and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Science categories.
Quantum mechanics had been started with the theory of the hydrogen atom, so when considering the quantum mechanics in Riemannian spaces it is natural to turn first to just this simplest system. A common quantum-mechanical hydrogen atom description is based materially on the assumption of the Euclidean character of the physical 3-space geometry. In this context, natural questions arise: what in the description is determined by this special assumption, and which changes will be entailed by allowing for other spatial geometries. The questions are of fundamental significance, even beyond their possible experimental testing. In the present book, detailed analytical treatment and exact solutions are given to a number of problems of quantum mechanics and field theory in simplest non-Euclidean spacetime models. The main attention is focused on new themes created by non-vanishing curvature in classical physical topics and concepts.