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1.

図書

図書
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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2.

図書

図書
Isaac Chavel
出版情報: Cambridge [England] : Cambridge University Press, 1995  xii, 386 p. ; 23 cm
シリーズ名: Cambridge tracts in mathematics ; 108
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目次情報: 続きを見る
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:
3.

図書

図書
edited by I. Chavel and H.M. Farkas
出版情報: Berlin ; Tokyo : Springer-Verlag, 1985  xii, 222 p., [1] leaf of plates ; 25 cm
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4.

図書

図書
Isaac Chavel
出版情報: Cambridge, UK ; New York : Cambridge University Press, c1993  xii, 386 p. ; 24 cm
シリーズ名: Cambridge tracts in mathematics ; 108
所蔵情報: loading…
目次情報: 続きを見る
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:
5.

図書

図書
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
所蔵情報: loading…
目次情報: 続きを見る
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:
6.

図書

図書
Isaac Chavel ; with a chapter by Burton Randol ; with appendix by Jozef Dodziuk
出版情報: Orlando ; Tokyo : Academic Press, 1984  xiv, 362 p. ; 24 cm
シリーズ名: Pure and applied mathematics ; 115
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目次情報: 続きを見る
Preface
The Laplacian
The Basic Examples
Curvature
Isoperimetric Inequalities
Eigenvalues and Kinematic Measure
The Heat Kernel for Compact Manifolds
The Dirichlet Heat Kernel for Regular Domains
The Heat Kernel for Noncompact Manifolds
Topological Perturbations with Negligible Effect
Surfaces of Constant Negative Curvature
The Selberg Trace Formula
Miscellanea
Laplacian on Forms
Bibliography
Index
Preface
The Laplacian
The Basic Examples
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