Spaces Of Constant Curvature
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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.
Spaces Of Constant Curvature
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Author : Joseph Albert Wolf
language : en
Publisher:
Release Date : 1977
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 1977 with Geometry, Riemannian categories.
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 Albert Wolf
language : en
Publisher:
Release Date : 1967
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 1967 with Geometry, Riemannian categories.
Riemannian Geometry
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Author : Takashi Sakai
language : en
Publisher: American Mathematical Soc.
Release Date : 1996-01-01
Riemannian Geometry written by Takashi Sakai 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 1996-01-01 with Mathematics categories.
This volume is an English translation of Sakai's textbook on Riemannian Geometry which was originally written in Japanese and published in 1992. The author's intent behind the original book was to provide to advanced undergraduate and graudate students an introduction to modern Riemannian geometry that could also serve as a reference. The book begins with an explanation of the fundamental notion of Riemannian geometry. Special emphasis is placed on understandability and readability, to guide students who are new to this area. The remaining chapters deal with various topics in Riemannian geometry, with the main focus on comparison methods and their applications.
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.
Spaces Of Constant Curvature
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Author : Joseph A. Wolf
language : it
Publisher:
Release Date : 1967
Spaces Of Constant Curvature written by Joseph A. Wolf and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1967 with categories.
Spaces Of Constant Curvature
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Author : Corey Anthony Hoelscher
language : en
Publisher:
Release Date : 2004
Spaces Of Constant Curvature written by Corey Anthony Hoelscher and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with categories.
Geometry Vi
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Author : M.M. Postnikov
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
Geometry Vi written by M.M. Postnikov 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.
The original Russian edition of this book is the fifth in my series "Lectures on Geometry. " Therefore, to make the presentation relatively independent and self-contained in the English translation, I have added supplementary chapters in a special addendum (Chaps. 3Q-36), in which the necessary facts from manifold theory and vector bundle theory are briefly summarized without proofs as a rule. In the original edition, the book is divided not into chapters but into lec tures. This is explained by its origin as classroom lectures that I gave. The principal distinction between chapters and lectures is that the material of each chapter should be complete to a certain extent and the length of chapters can differ, while, in contrast, all lectures should be approximately the same in length and the topic of any lecture can change suddenly in the middle. For the series "Encyclopedia of Mathematical Sciences," the origin of a book has no significance, and the name "chapter" is more usual. Therefore, the name of subdivisions was changed in the translation, although no structural surgery was performed. I have also added a brief bibliography, which was absent in the original edition. The first ten chapters are devoted to the geometry of affine connection spaces. In the first chapter, I present the main properties of geodesics in these spaces. Chapter 2 is devoted to the formalism of covariant derivatives, torsion tensor, and curvature tensor. The major part of Chap.
Sources Of Hyperbolic Geometry
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Author : John Stillwell
language : en
Publisher: American Mathematical Soc.
Release Date : 1996
Sources Of Hyperbolic Geometry written by John Stillwell 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 1996 with Mathematics categories.
This book presents, for the first time in English, the papers of Beltrami, Klein, and Poincare that brought hyperbolic geometry into the mainstream of mathematics. A recognition of Beltrami comparable to that given the pioneering works of Bolyai and Lobachevsky seems long overdue - not only because Beltrami rescued hyperbolic geometry from oblivion by proving it to be logically consistent, but because he gave it a concrete meaning (a model) that made hyperbolic geometry part of ordinary mathematics. The models subsequently discovered by Klein and Poincare brought hyperbolic geometry even further down to earth and paved the way for the current explosion of activity in low-dimensional geometry and topology.By placing the works of these three mathematicians side by side and providing commentaries, this book gives the student, historian, or professional geometer a bird's-eye view of one of the great episodes in mathematics. The unified setting and historical context reveal the insights of Beltrami, Klein, and Poincare in their full brilliance.