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Author | : G. Daniel Mostow |
Publisher | : Princeton University Press |
Total Pages | : 204 |
Release | : 1973-12-21 |
Genre | : Mathematics |
ISBN | : 0691081360 |
Download Strong Rigidity of Locally Symmetric Spaces Book in PDF, ePub and Kindle
Locally symmetric spaces are generalizations of spaces of constant curvature. In this book the author presents the proof of a remarkable phenomenon, which he calls "strong rigidity": this is a stronger form of the deformation rigidity that has been investigated by Selberg, Calabi-Vesentini, Weil, Borel, and Raghunathan. The proof combines the theory of semi-simple Lie groups, discrete subgroups, the geometry of E. Cartan's symmetric Riemannian spaces, elements of ergodic theory, and the fundamental theorem of projective geometry as applied to Tit's geometries. In his proof the author introduces two new notions having independent interest: one is "pseudo-isometries"; the other is a notion of a quasi-conformal mapping over the division algebra K (K equals real, complex, quaternion, or Cayley numbers). The author attempts to make the account accessible to readers with diverse backgrounds, and the book contains capsule descriptions of the various theories that enter the proof.
Author | : G. Daniel Mostow |
Publisher | : Princeton University Press |
Total Pages | : 204 |
Release | : 2016-03-02 |
Genre | : Mathematics |
ISBN | : 1400881838 |
Download Strong Rigidity of Locally Symmetric Spaces. (AM-78), Volume 78 Book in PDF, ePub and Kindle
Locally symmetric spaces are generalizations of spaces of constant curvature. In this book the author presents the proof of a remarkable phenomenon, which he calls "strong rigidity": this is a stronger form of the deformation rigidity that has been investigated by Selberg, Calabi-Vesentini, Weil, Borel, and Raghunathan. The proof combines the theory of semi-simple Lie groups, discrete subgroups, the geometry of E. Cartan's symmetric Riemannian spaces, elements of ergodic theory, and the fundamental theorem of projective geometry as applied to Tit's geometries. In his proof the author introduces two new notions having independent interest: one is "pseudo-isometries"; the other is a notion of a quasi-conformal mapping over the division algebra K (K equals real, complex, quaternion, or Cayley numbers). The author attempts to make the account accessible to readers with diverse backgrounds, and the book contains capsule descriptions of the various theories that enter the proof.
Author | : Ka Fai Li |
Publisher | : |
Total Pages | : 208 |
Release | : 2012 |
Genre | : Complex manifolds |
ISBN | : |
Download Rigidity Theorems on Hermitian Locally Symmetric Spaces Book in PDF, ePub and Kindle
By using Bochner technique of harmonic maps, Siu[15, 16] proved a strong rigidity theorem concerning the complex structure of compact quotients of irreducible bounded symmetric domain of complex dimension≥ 2. Later in [9], Mok proved a metric rigidity theorem which asserts that any Hermitian metric of seminegative holomorphic bisectional curvature on a compact quotient of an irreducible bounded symmetric domain of rank≥ 2 is necessarily a constant multiple of the canonical metric. This theorem together with the theorem of Siu yields a generalization of a special case of Mostow's rigidity theorem[14]. This thesis is an exposition of Mok's results.
Author | : Ngaiming Mok |
Publisher | : World Scientific |
Total Pages | : 296 |
Release | : 1989 |
Genre | : Mathematics |
ISBN | : 9789971508029 |
Download Metric Rigidity Theorems on Hermitian Locally Symmetric Manifolds Book in PDF, ePub and Kindle
This monograph studies the problem of characterizing canonical metrics on Hermitian locally symmetric manifolds X of non-compact/compact types in terms of curvature conditions. The proofs of these metric rigidity theorems are applied to the study of holomorphic mappings between manifolds X of the same type. Moreover, a dual version of the generalized Frankel Conjecture on characterizing compact Khler manifolds are also formulated.
Author | : Lizhen Ji |
Publisher | : American Mathematical Soc. |
Total Pages | : 282 |
Release | : 2008 |
Genre | : Mathematics |
ISBN | : 0821848666 |
Download Arithmetic Groups and Their Generalizations Book in PDF, ePub and Kindle
In one guise or another, many mathematicians are familiar with certain arithmetic groups, such as $\mathbf{Z}$ or $\textrm{SL}(n, \mathbf{Z})$. Yet, many applications of arithmetic groups and many connections to other subjects within mathematics are less well known. Indeed, arithmetic groups admit many natural and important generalizations. The purpose of this expository book is to explain, through some brief and informal comments and extensive references, what arithmetic groups and their generalizations are, why they are important to study, and how they can be understood and applied to many fields, such as analysis, geometry, topology, number theory, representation theory, and algebraic geometry. It is hoped that such an overview will shed a light on the important role played by arithmetic groups in modern mathematics. Titles in this series are co-published with International Press, Cambridge, MA.Table of Contents: Introduction; General comments on references; Examples of basic arithmetic groups; General arithmetic subgroups and locally symmetric spaces; Discrete subgroups of Lie groups and arithmeticity of lattices in Lie groups; Different completions of $\mathbb{Q}$ and $S$-arithmetic groups over number fields; Global fields and $S$-arithmetic groups over function fields; Finiteness properties of arithmetic and $S$-arithmetic groups; Symmetric spaces, Bruhat-Tits buildings and their arithmetic quotients; Compactifications of locally symmetric spaces; Rigidity of locally symmetric spaces; Automorphic forms and automorphic representations for general arithmetic groups; Cohomology of arithmetic groups; $K$-groups of rings of integers and $K$-groups of group rings; Locally homogeneous manifolds and period domains; Non-cofinite discrete groups, geometrically finite groups; Large scale geometry of discrete groups; Tree lattices; Hyperbolic groups; Mapping class groups and outer automorphism groups of free groups; Outer automorphism group of free groups and the outer spaces; References; Index. Review from Mathematical Reviews: ...the author deserves credit for having done the tremendous job of encompassing every aspect of arithmetic groups visible in today's mathematics in a systematic manner; the book should be an important guide for some time to come.(AMSIP/43.
Author | : Armand Borel |
Publisher | : Springer Science & Business Media |
Total Pages | : 477 |
Release | : 2006-07-25 |
Genre | : Mathematics |
ISBN | : 0817644660 |
Download Compactifications of Symmetric and Locally Symmetric Spaces Book in PDF, ePub and Kindle
Introduces uniform constructions of most of the known compactifications of symmetric and locally symmetric spaces, with emphasis on their geometric and topological structures Relatively self-contained reference aimed at graduate students and research mathematicians interested in the applications of Lie theory and representation theory to analysis, number theory, algebraic geometry and algebraic topology
Author | : Yves Guivarc'h |
Publisher | : Springer Science & Business Media |
Total Pages | : 310 |
Release | : 1998-08-26 |
Genre | : Mathematics |
ISBN | : 9780817638993 |
Download Compactifications of Symmetric Spaces Book in PDF, ePub and Kindle
The concept of symmetric space is of central importance in many branches of mathematics. Compactifications of these spaces have been studied from the points of view of representation theory, geometry, and random walks. This work is devoted to the study of the interrelationships among these various compactifications and, in particular, focuses on the martin compactifications. It is the first exposition to treat compactifications of symmetric spaces systematically and to uniformized the various points of view. The work is largely self-contained, with comprehensive references to the literature. It is an excellent resource for both researchers and graduate students.
Author | : Werner Ballmann |
Publisher | : Springer Science & Business Media |
Total Pages | : 280 |
Release | : 2013-12-11 |
Genre | : Mathematics |
ISBN | : 1468491598 |
Download Manifolds of Nonpositive Curvature Book in PDF, ePub and Kindle
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.
Author | : Jürgen Jost |
Publisher | : Springer Science & Business Media |
Total Pages | : 406 |
Release | : 2013-04-17 |
Genre | : Mathematics |
ISBN | : 3662031183 |
Download Riemannian Geometry and Geometric Analysis Book in PDF, ePub and Kindle
The present textbook is a somewhat expanded version of the material of a three-semester course I gave in Bochum. It attempts a synthesis of geometric and analytic methods in the study of Riemannian manifolds. In the first chapter, we introduce the basic geometric concepts, like dif ferentiable manifolds, tangent spaces, vector bundles, vector fields and one parameter groups of diffeomorphisms, Lie algebras and groups and in par ticular Riemannian metrics. We also derive some elementary results about geodesics. The second chapter introduces de Rham cohomology groups and the es sential tools from elliptic PDE for treating these groups. In later chapters, we shall encounter nonlinear versions of the methods presented here. The third chapter treats the general theory of connections and curvature. In the fourth chapter, we introduce Jacobi fields, prove the Rauch com parison theorems for Jacobi fields and apply these results to geodesics. These first four chapters treat the more elementary and basic aspects of the subject. Their results will be used in the remaining, more advanced chapters that are essentially independent of each other. In the fifth chapter, we develop Morse theory and apply it to the study of geodesics. The sixth chapter treats symmetric spaces as important examples of Rie mannian manifolds in detail.
Author | : Robert Everist Greene |
Publisher | : American Mathematical Soc. |
Total Pages | : 585 |
Release | : 1993 |
Genre | : Mathematics |
ISBN | : 082181494X |
Download Differential Geometry: Partial Differential Equations on Manifolds Book in PDF, ePub and Kindle
The first of three parts comprising Volume 54, the proceedings of the Summer Research Institute on Differential Geometry, held at the University of California, Los Angeles, July 1990 (ISBN for the set is 0-8218-1493-1). Part 1 begins with a problem list by S.T. Yau, successor to his 1980 list ( Sem