Riemannian geometry : a modern introduction

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Riemannian geometry : a modern introduction / Isaac Chavel

版:: 2nd ed
資料種別:: 図書
出版情報:: New York : Cambridge University Press, 2006
形態:: xvi, 471 p. ; 24 cm
シリーズ名:: Cambridge studies in advanced mathematics ; 98 <BA00109761>
著者名:: Chavel, Isaac <DA00238658>
ISBN:: 9780521853682 [0521853680] (: hbk)
9780521619547 [0521619548] (: pbk)
書誌ID:: BA77310117

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他の版・巻

Riemannian geometry : a modern introduction. 1st pbk. ed. with corr (: pbk)
Isaac Chavel , Cambridge University Press , 1995

Riemannian geometry : a modern introduction (: pbk)
Isaac Chavel , Cambridge University Press , c1993

書誌詳細

注記:

Includes bibliographical references (p. 449-464) and indexes

主題:

Geometry, Riemannian

言語:

英語

目次情報:

Preface to the Second Edition

Preface

Riemannian Manifolds / I：

Connections / I.1：

Parallel Translation of Vector Fields / I.2：

Geodesics and the Exponential Map / I.3：

The Torsion and Curvature Tensors / I.4：

Riemannian Metrics / I.5：

The Metric Space Structure / I.6：

Geodesics and Completeness / I.7：

Calculations with Moving Frames / I.8：

Notes and Exercises / I.9：

Riemannian Curvature / II：

The Riemann Sectional Curvature / II.1：

Riemannian Submanifolds / II.2：

Spaces of Constant Sectional Curvature / II.3：

First and Second Variations of Arc Length / II.4：

Jacobi's Equation and Criteria / II.5：

Elementary Comparison Theorems / II.6：

Jacobi Fields and the Exponential Map / II.7：

Riemann Normal Coordinates / II.8：

Riemannian Volume / II.9：

Geodesic Spherical Coordinates / III.1：

The Conjugate and Cut Loci / III.2：

Riemannian Measure / III.3：

Volume Comparison Theorems / III.4：

The Area of Spheres / III.5：

Fermi Coordinates / III.6：

Integration of Differential Forms / III.7：

Appendix: Eigenvalue Comparison Theorems / III.8：

Riemannian Coverings / IV：

The Fundamental Group / IV.1：

Volume Growth of Riemannian Coverings / IV.3：

Discretization of Riemannian Manifolds / IV.4：

The Free Homotopy Classes / IV.5：

Surfaces / IV.6：

Systolic Inequalities / V.1：

Gauss-Bonnet Theory of Surfaces / V.2：

The Collar Theorem / V.3：

The Isoperimetric Problem: Introduction / V.4：

Surfaces with Curvature Bounded from Above / V.5：

The Isoperimetric Problem on the Paraboloid of Revolution / V.6：

Isoperimetric Inequalities (Constant Curvature) / V.7：

The Brunn-Minkowski Theorem / VI.1：

Solvability of a Neumann Problem in R[superscript n] / VI.2：

Fermi Coordinates in Constant Sectional Curvature Spaces / VI.3：

Spherical Symmetrization and Isoperimetric Inequalities / VI.4：

M. Gromov's Uniqueness Proof - Euclidean and Hyperbolic Space / VI.5：

The Isoperimetric Inequality on Spheres / VI.6：

The Kinematic Density / VI.7：

The Differential Geometry of Analytical Dynamics / VII.1：

The Berger-Kazdan Inequalities / VII.2：

On Manifolds with No Conjugate Points / VII.3：

Santalo's Formula / VII.4：

Isoperimetric Inequalities (Variable Curvature) / VII.5：

Croke's Isoperimetric Inequality / VIII.1：

Buser's Isoperimetric Inequality / VIII.2：

Isoperimetric Constants / VIII.3：

Discretizations and Isoperimetry / VIII.4：

Comparison and Finiteness Theorems / VIII.5：

Preliminaries / IX.1：

H. E. Rauch's Comparison Theorem / IX.2：

Comparison Theorems with Initial Submanifolds / IX.3：

Refinements of the Rauch Theorem / IX.4：

Triangle Comparison Theorems / IX.5：

Convexity / IX.6：

Center of Mass / IX.7：

Cheeger's Finiteness Theorem / IX.8：

Hints and Sketches for Exercises / IX.9：

Hints and Sketches: Chapter I

Hints and Sketches: Chapter II

Hints and Sketches: Chapter III

Hints and Sketches: Chapter IV

Hints and Sketches: Chapter V

Hints and Sketches: Chapter VI

Hints and Sketches: Chapter VII

Hints and Sketches: Chapter VIII

Hints and Sketches: Chapter IX

Bibliography

Author Index

Subject Index

Preface to the Second Edition

Preface

Riemannian Manifolds / I：

Connections / I.1：

Parallel Translation of Vector Fields / I.2：

Geodesics and the Exponential Map / I.3：

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