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図書
図書
1. Riemannian geometry : a modern introduction. 2nd ed (: hbk ; : pbk)
Isaac Chavel
出版情報: New York : Cambridge University Press, 2006  xvi, 471 p. ; 24 cm
シリーズ名: Cambridge studies in advanced mathematics ; 98
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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：
2.

図書
図書
2. Isoperimetric inequalities : differential geometric and analytic perspectives (: hbk)
Isaac Chavel
出版情報: Cambridge : Cambridge University Press, 2001  xii, 268 p. ; 24 cm
シリーズ名: Cambridge tracts in mathematics ; 145
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