Geometry Of Nonpositively Curved Manifolds
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Geometry Of Nonpositively Curved Manifolds
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Author : Patrick Eberlein
language : en
Publisher: University of Chicago Press
Release Date : 1996
Geometry Of Nonpositively Curved Manifolds written by Patrick Eberlein and has been published by University of Chicago Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with Mathematics categories.
Starting from the foundations, the author presents an almost entirely self-contained treatment of differentiable spaces of nonpositive curvature, focusing on the symmetric spaces in which every geodesic lies in a flat Euclidean space of dimension at least two. The book builds to a discussion of the Mostow Rigidity Theorem and its generalizations, and concludes by exploring the relationship in nonpositively curved spaces between geometric and algebraic properties of the fundamental group. This introduction to the geometry of symmetric spaces of non-compact type will serve as an excellent guide for graduate students new to the material, and will also be a useful reference text for mathematicians already familiar with the subject.
Manifolds Of Nonpositive Curvature
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Author : Werner Ballmann
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-11
Manifolds Of Nonpositive Curvature written by Werner Ballmann 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 2013-12-11 with Mathematics categories.
This volume presents a complete and self-contained description of new results in the theory of manifolds of nonpositive curvature. It is based on lectures delivered by M. Gromov at the Collège de France in Paris. Therefore this book may also serve as an introduction to the subject of nonpositively curved manifolds. The latest progress in this area is reflected in the article of W. Ballmann describing the structure of manifolds of higher rank.
Lectures On Spaces Of Nonpositive Curvature
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Author : Werner Ballmann
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Lectures On Spaces Of Nonpositive Curvature written by Werner Ballmann and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
Singular spaces with upper curvature bounds and, in particular, spaces of nonpositive curvature, have been of interest in many fields, including geometric (and combinatorial) group theory, topology, dynamical systems and probability theory. In the first two chapters of the book, a concise introduction into these spaces is given, culminating in the Hadamard-Cartan theorem and the discussion of the ideal boundary at infinity for simply connected complete spaces of nonpositive curvature. In the third chapter, qualitative properties of the geodesic flow on geodesically complete spaces of nonpositive curvature are discussed, as are random walks on groups of isometries of nonpositively curved spaces. The main class of spaces considered should be precisely complementary to symmetric spaces of higher rank and Euclidean buildings of dimension at least two (Rank Rigidity conjecture). In the smooth case, this is known and is the content of the Rank Rigidity theorem. An updated version of the proof of the latter theorem (in the smooth case) is presented in Chapter IV of the book. This chapter contains also a short introduction into the geometry of the unit tangent bundle of a Riemannian manifold and the basic facts about the geodesic flow. In an appendix by Misha Brin, a self-contained and short proof of the ergodicity of the geodesic flow of a compact Riemannian manifold of negative curvature is given. The proof is elementary and should be accessible to the non-specialist. Some of the essential features and problems of the ergodic theory of smooth dynamical systems are discussed, and the appendix can serve as an introduction into this theory.
Manifolds Of Nonpositive Curvature
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Author : Werner Ballmann
language : en
Publisher:
Release Date : 1985
Manifolds Of Nonpositive Curvature written by Werner Ballmann and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985 with Geometry, Differential categories.
Nonpositive Curvature
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Author : Jürgen Jost
language : en
Publisher: Birkhauser
Release Date : 1997
Nonpositive Curvature written by Jürgen Jost and has been published by Birkhauser this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with Geometry, Differential categories.
This book discusses various geometric and analytic aspects of nonpositive curvature, starting with a discussion of Riemannian examples and rigidity theorems. It then treats generalized notions of nonpositive curvature in metric geometry in the sense of Alexandrov and Busemann, as well as the theory of harmonic maps with values in such spaces. It is intended for researchers and graduate students in Riemannian and metric geometry as well as calculus of variations.
Geometry Of Nonpositively Curved Manifolds
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Author : Patrick B. Eberlein
language : en
Publisher: University of Chicago Press
Release Date : 1997-04-01
Geometry Of Nonpositively Curved Manifolds written by Patrick B. Eberlein and has been published by University of Chicago Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-04-01 with Mathematics categories.
Starting from the foundations, the author presents an almost entirely self-contained treatment of differentiable spaces of nonpositive curvature, focusing on the symmetric spaces in which every geodesic lies in a flat Euclidean space of dimension at least two. The book builds to a discussion of the Mostow Rigidity Theorem and its generalizations, and concludes by exploring the relationship in nonpositively curved spaces between geometric and algebraic properties of the fundamental group. This introduction to the geometry of symmetric spaces of non-compact type will serve as an excellent guide for graduate students new to the material, and will also be a useful reference text for mathematicians already familiar with the subject.
Manifolds Of Nonpositive Curvature
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Author : Werner Ballmann
language : en
Publisher:
Release Date : 2014-09-01
Manifolds Of Nonpositive Curvature written by Werner Ballmann and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-09-01 with categories.
Geometry Of Manifolds With Non Negative Sectional Curvature
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Author : Owen Dearricott
language : en
Publisher: Springer
Release Date : 2014-07-22
Geometry Of Manifolds With Non Negative Sectional Curvature written by Owen Dearricott and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-22 with Mathematics categories.
Providing an up-to-date overview of the geometry of manifolds with non-negative sectional curvature, this volume gives a detailed account of the most recent research in the area. The lectures cover a wide range of topics such as general isometric group actions, circle actions on positively curved four manifolds, cohomogeneity one actions on Alexandrov spaces, isometric torus actions on Riemannian manifolds of maximal symmetry rank, n-Sasakian manifolds, isoparametric hypersurfaces in spheres, contact CR and CR submanifolds, Riemannian submersions and the Hopf conjecture with symmetry. Also included is an introduction to the theory of exterior differential systems.
Metric Spaces Of Non Positive Curvature
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Author : Martin R. Bridson
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Metric Spaces Of Non Positive Curvature written by Martin R. Bridson 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 2013-03-09 with Mathematics categories.
A description of the global properties of simply-connected spaces that are non-positively curved in the sense of A. D. Alexandrov, and the structure of groups which act on such spaces by isometries. The theory of these objects is developed in a manner accessible to anyone familiar with the rudiments of topology and group theory: non-trivial theorems are proved by concatenating elementary geometric arguments, and many examples are given. Part I provides an introduction to the geometry of geodesic spaces, while Part II develops the basic theory of spaces with upper curvature bounds. More specialized topics, such as complexes of groups, are covered in Part III.
From Riches To Raags 3 Manifolds Right Angled Artin Groups And Cubical Geometry
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Author : Daniel T. Wise
language : en
Publisher: American Mathematical Soc.
Release Date : 2012
From Riches To Raags 3 Manifolds Right Angled Artin Groups And Cubical Geometry written by Daniel T. Wise 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 2012 with Mathematics categories.
Wise describes a stream of geometric group theory connecting many of the classically considered groups arising in combinatorial group theory with right-angled Artin groups. He writes for new or seasoned researchers who have completed at least an introductory course of geometric groups theory or even just hyperbolic groups, but says some comfort with graphs of groups would be helpful. His topics include non-positively curved cube complexes, virtual specialness of malnormal amalgams, finiteness properties of the dual cube complex, walls in cubical small-cancellation theory, and hyperbolicity and quasiconvexity detection. Color drawings illustrate. Annotation ©2013 Book News, Inc., Portland, OR (booknews.com).