Homogeneous Manifolds With Negative Curvature Part Ii

Author : Robert Azencott,Edward N. Wilson
Publisher : American Mathematical Soc.
Page : 102 pages
File Size : 55,7 Mb
Release : 1976
Category : Mathematics
ISBN : 9780821821787

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Homogeneous Manifolds with Negative Curvature, Part II by Robert Azencott,Edward N. Wilson Pdf

This paper is the second in a series dealing with the structure of the full isometry group I(M) for M a connected, simply connected, homogeneous, Riemannian manifold with non-positive sectional curvature. It is shown that every such manifold determines canonically a conjugacy class of subgroups of I(M) which act simply transitively on M. The class of all simply transitive subgroups of I(M) is identified and it is demonstrated that an arbitrary simply transitive subgroup may be modified slightly to produce a subgroup in the canonical class. The class of all connected Lie groups G for which there exists such a manifold M with G isomorphic to the identity connected component of I(M) is identified by means of a list of structural conditions on the Lie algebra of G. Given an arbitrary connected, simply connected Riemannian manifold M together with a given simply transitive group S of isometries, an algorithm is exhibited to explicitly compute the Lie algebra of I(M) from the transported Riemannian data on S.

Author : Peter B. Gilkey
Publisher : World Scientific
Page : 389 pages
File Size : 55,5 Mb
Release : 2007
Category : Science
ISBN : 9781860947858

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The Geometry of Curvature Homogeneous Pseudo-Riemannian Manifolds by Peter B. Gilkey Pdf

"Pseudo-Riemannian geometry is an active research field not only in differential geometry but also in mathematical physics where the higher signature geometries play a role in brane theory. An essential reference tool for research mathematicians and physicists, this book also serves as a useful introduction to students entering this active and rapidly growing field. The author presents a comprehensive treatment of several aspects of pseudo-Riemannian geometry, including the spectral geometry of the curvature tensor, curvature homogeneity, and Stanilov-Tsankov-Videv theory."--BOOK JACKET.

Author : F. Tricerri,L. Vanhecke
Publisher : Cambridge University Press
Page : 145 pages
File Size : 42,5 Mb
Release : 1983-06-23
Category : Mathematics
ISBN : 9780521274890

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Homogeneous Structures on Riemannian Manifolds by F. Tricerri,L. Vanhecke Pdf

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.

Author : Anonim
Publisher : Unknown
Page : 474 pages
File Size : 40,7 Mb
Release : 1977
Category : Engineering
ISBN : PURD:32754081541025

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Summaries of Projects Completed in Fiscal Year ... by Anonim Pdf

Author : National Science Foundation (U.S.)
Publisher : Unknown
Page : 488 pages
File Size : 44,5 Mb
Release : 2024-06-18
Category : Engineering
ISBN : STANFORD:36105029358830

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Summaries of Projects Completed by National Science Foundation (U.S.) Pdf

Author : National Science Foundation (U.S.)
Publisher : Unknown
Page : 476 pages
File Size : 41,9 Mb
Release : 1977
Category : Engineering
ISBN : UIUC:30112050131090

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Summaries of Projects Completed in Fiscal Year ... by National Science Foundation (U.S.) Pdf

Author : A. B. Katok
Publisher : American Mathematical Soc.
Page : 895 pages
File Size : 44,7 Mb
Release : 2001
Category : Ergodic theory
ISBN : 9780821826829

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Smooth Ergodic Theory and Its Applications by A. B. Katok Pdf

During the past decade, there have been several major new developments in smooth ergodic theory, which have attracted substantial interest to the field from mathematicians as well as scientists using dynamics in their work. In spite of the impressive literature, it has been extremely difficult for a student-or even an established mathematician who is not an expert in the area-to acquire a working knowledge of smooth ergodic theory and to learn how to use its tools. Accordingly, the AMS Summer Research Institute on Smooth Ergodic Theory and Its Applications (Seattle, WA) had a strong educational component, including ten mini-courses on various aspects of the topic that were presented by leading experts in the field. This volume presents the proceedings of that conference. Smooth ergodic theory studies the statistical properties of differentiable dynamical systems, whose origin traces back to the seminal works of Poincare and later, many great mathematicians who made contributions to the development of the theory. The main topic of this volume, smooth ergodic theory, especially the theory of nonuniformly hyperbolic systems, provides the principle paradigm for the rigorous study of complicated or chaotic behavior in deterministic systems. This paradigm asserts that if a non-linear dynamical system exhibits sufficiently pronounced exponential behavior, then global properties of the system can be deduced from studying the linearized system. One can then obtain detailed information on topological properties (such as the growth of periodic orbits, topological entropy, and dimension of invariant sets including attractors), as well as statistical properties (such as the existence of invariant measures, asymptotic behavior of typical orbits, ergodicity, mixing, decay of corre This volume serves a two-fold purpose: first, it gives a useful gateway to smooth ergodic theory for students and nonspecialists, and second, it provides a state-of-the-art report on important current aspects of the subject. The book is divided into three parts: lecture notes consisting of three long expositions with proofs aimed to serve as a comprehensive and self-contained introduction to a particular area of smooth ergodic theory; thematic sections based on mini-courses or surveys held at the conference; and original contributions presented at the meeting or closely related to the topics that were discussed there.

Author : Anonim
Publisher : Unknown
Page : 740 pages
File Size : 40,5 Mb
Release : 1989
Category : Electronic journals
ISBN : UCAL:B3053874

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Illinois Journal of Mathematics by Anonim Pdf

Author : Robert Brooks,Carolyn Gordon,Peter A. Perry
Publisher : American Mathematical Soc.
Page : 299 pages
File Size : 43,7 Mb
Release : 1994
Category : Mathematics
ISBN : 9780821851852

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Geometry of the Spectrum by Robert Brooks,Carolyn Gordon,Peter A. Perry Pdf

Spectral geometry runs through much of contemporary mathematics, drawing on and stimulating developments in such diverse areas as Lie algebras, graph theory, group representation theory, and Riemannian geometry. The aim is to relate the spectrum of the Laplace operator or its graph-theoretic analogue, the adjacency matrix, to underlying geometric and topological data. This volume brings together papers presented at the AMS-IMS-SIAM Joint Summer Research Conference on Spectral Geometry, held in July 1993 at the University of Washington in Seattle. With contributions from some of the top experts in the field, this book presents an excellent overview of current developments in spectral geometry.

Author : Valerii Berestovskii,Yurii Nikonorov
Publisher : Springer Nature
Page : 482 pages
File Size : 40,8 Mb
Release : 2020-11-05
Category : Mathematics
ISBN : 9783030566586

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Riemannian Manifolds and Homogeneous Geodesics by Valerii Berestovskii,Yurii Nikonorov Pdf

This book is devoted to Killing vector fields and the one-parameter isometry groups of Riemannian manifolds generated by them. It also provides a detailed introduction to homogeneous geodesics, that is, geodesics that are integral curves of Killing vector fields, presenting both classical and modern results, some very recent, many of which are due to the authors. The main focus is on the class of Riemannian manifolds with homogeneous geodesics and on some of its important subclasses. To keep the exposition self-contained the book also includes useful general results not only on geodesic orbit manifolds, but also on smooth and Riemannian manifolds, Lie groups and Lie algebras, homogeneous Riemannian manifolds, and compact homogeneous Riemannian spaces. The intended audience is graduate students and researchers whose work involves differential geometry and transformation groups.

Author : W H Chen,C P Wang,A-M Li,U Simon,M Wiehe,L Verstraelen
Publisher : World Scientific
Page : 360 pages
File Size : 51,8 Mb
Release : 2000-11-07
Category : Mathematics
ISBN : 9789814492034

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Geometry and Topology of Submanifolds X by W H Chen,C P Wang,A-M Li,U Simon,M Wiehe,L Verstraelen Pdf

Contents:Progress in Affine Differential Geometry — Problem List and Continued Bibliography (T Binder & U Simon)On the Classification of Timelike Bonnet Surfaces (W H Chen & H Z Li)Affine Hyperspheres with Constant Affine Sectional Curvature (F Dillen et al.)Geometric Properties of the Curvature Operator (P Gilkey)On a Question of S S Chern Concerning Minimal Hypersurfaces of Spheres (I Hiric( & L Verstraelen)Parallel Pure Spinors on Pseudo-Riemannian Manifolds (I Kath)Twistorial Construction of Spacelike Surfaces in Lorentzian 4-Manifolds (F Leitner)Nirenberg's Problem in 90's (L Ma)A New Proof of the Homogeneity of Isoparametric Hypersurfaces with (g,m) = (6, 1) (R Miyaoka)Harmonic Maps and Negatively Curved Homogeneous Spaces (S Nishikawa)Biharmonic Morphisms Between Riemannian Manifolds (Y L Ou)Intrinsic Properties of Real Hypersurfaces in Complex Space Forms (P J Ryan)On the Nonexistence of Stable Minimal Submanifolds in Positively Pinched Riemannian Manifolds (Y B Shen & H Q Xu)Geodesic Mappings of the Ellipsoid (K Voss)η-Invariants and the Poincaré-Hopf Index Formula (W Zhang)and other papers Readership: Researchers in differential geometry and topology. Keywords:Conference;Proceedings;Berlin (Germany);Beijing (China);Geometry;Topology;Submanifolds X;Differential Geometry;Dedication

Author : Julia Plehnert
Publisher : Logos Verlag Berlin GmbH
Page : 94 pages
File Size : 48,5 Mb
Release : 2012
Category : Mathematics
ISBN : 9783832532062

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Constant Mean Curvature Surfaces in Homogeneous Manifolds by Julia Plehnert Pdf

In this dissertation new constant mean curvature surfaces in homogeneous 3-manifolds are constructed. They arise as sister surfaces of Plateau solutions. The first example, a two-parameter family of MC H surfaces in ∑(k) x R with H ∈ [0,1/2] and k + 4H2 ≤ 0, has genus 0,2 k ends and k-fold dihedral symmetry, k ≥ 2. The existence of the minimal sister follows from the construction of a mean convex domain. The projection of the domain is non-convex. The second example is an MC 1/2 surface in H2 ∈ R with k ends, genus 1 and k-fold dihedral symmetry, k ≥ 3. One has to solve two period problems in the construction. The first period guarantees that the surface has exactly one horizontal symmetry. For the second period the control of a horizontal mirror curve proves the dihedral symmetry. For H=1/2 all surfaces are Alexandrov-embedded.

Author : John Willard Milnor
Publisher : American Mathematical Soc.
Page : 312 pages
File Size : 50,7 Mb
Release : 1994
Category : Algebra
ISBN : 0914098306

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Geometry by John Willard Milnor Pdf

This volume is the seventh in the series Collected Papers of John Milnor. Together with the preceding Volume VI, it contains all of Milnor's papers in dynamics, through the year 2012. Most of the papers are in holomorphic dynamics; however, there are two in real dynamics and one on cellular automata. Two of the papers are published here for the first time. The papers in this volume provide important and fundamental material in real and complex dynamical systems. Many have become classics, and have inspired further research in the field. Some of the questions addressed here continue to be important in current research. In some cases, there have been minor corrections or clarifications, as well as references to more recent work which answers questions raised by the author. The volume also includes an index to facilitate searching the book for specific topics.

Author : Eric Boeckx,Lieven Vanhecke,Oldrich Kowalski
Publisher : World Scientific
Page : 320 pages
File Size : 46,9 Mb
Release : 1996-11-09
Category : Mathematics
ISBN : 9789814498555

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Riemannian Manifolds of Conullity Two by Eric Boeckx,Lieven Vanhecke,Oldrich Kowalski Pdf

This book deals with Riemannian manifolds for which the nullity space of the curvature tensor has codimension two. These manifolds are “semi-symmetric spaces foliated by Euclidean leaves of codimension two” in the sense of Z I Szabó. The authors concentrate on the rich geometrical structure and explicit descriptions of these remarkable spaces. Also parallel theories are developed for manifolds of “relative conullity two”. This makes a bridge to a survey on curvature homogeneous spaces introduced by I M Singer. As an application of the main topic, interesting hypersurfaces with type number two in Euclidean space are discovered, namely those which are locally rigid or “almost rigid”. The unifying method is solving explicitly particular systems of nonlinear PDE. Contents:IntroductionDefinition of Semi-Symmetric Spaces and Early DevelopmentLocal Structure of Semi-Symmetric SpacesExplicit Treatment of Foliated Semi-Symmetric SpacesCurvature Homogeneous Semi-Symmetric SpacesAsymptotic Foliations and Algebraic RankThree-Dimensional Riemannian Manifolds of Conullity TwoAsymptotically Foliated Semi-Symmetric SpacesElliptic Semi-Symmetric SpacesComplete Foliated Semi-Symmetric SpacesApplication: Local Rigidity Problems for Hypersurfaces with Type Number Two in IR4Three-Dimensional Riemannian Manifolds of c-Conullity TwoMore about Curvature Homogeneous SpacesBiolographyIndex Readership: Mathematicians and mathematical physicists. keywords:Riemannian Manifold;Curvature Homogeneous Space;Semi-Symmetric Space;Pseudo-Symmetric Space;Asymptotic Foliation;Hypersurface with Type Number Two;Gromov Conjecture;Lichnerowicz Formula;Nomizu Conjecture;Singer Number

Author : John Bland,Kang-Tae Kim,Steven George Krantz
Publisher : American Mathematical Soc.
Page : 338 pages
File Size : 48,9 Mb
Release : 2003
Category : Differential geometry
ISBN : 9780821832738

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Explorations in Complex and Riemannian Geometry by John Bland,Kang-Tae Kim,Steven George Krantz Pdf

This book contains contributions by an impressive list of leading mathematicians. The articles include high-level survey and research papers exploring contemporary issues in geometric analysis, differential geometry, and several complex variables. Many of the articles will provide graduate students with a good entry point into important areas of modern research. The material is intended for researchers and graduate students interested in several complex variables and complex geometry.