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1.

図書
図書
1. Riemannian geometry and geometric analysis. 2nd ed
Jürgen Jost
出版情報: Berlin ; New York : Springer, c1998  xiii, 455 p. ; 24 cm
シリーズ名: Universitext
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2.

図書
図書
2. Riemannian geometry and geometric analysis (: us ; : gw)
Jürgen Jost
出版情報: Berlin ; New York : Springer-Verlag, c1995  xi, 401 p. ; 24 cm
シリーズ名: Universitext
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3.

図書
図書
3. Riemannian geometry and geometric analysis. 3rd ed
Jürgen Jost
出版情報: Berlin : Springer, c2002  xiii, 532 p. ; 24 cm
シリーズ名: Universitext
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目次情報: 続きを見る
Foundational Material / 1：
Manifolds and Di erentiable Manifolds / 1.1：
Tangent Spaces / 1.2：
Submanifolds / 1.3：
Riemannian Metrics / 1.4：
Vector Bundles / 1.5：
Integral Curves of Vector Fields. Lie Algebras / 1.6：
Lie Groups / 1.7：
Spin Structures / 1.8：
Exercises for Chapter 1
De Rham Cohomology and Harmonic Dierential Forms / 2：
The Laplace Operator / 2.1：
Representing Cohomology Classes by Harmonic Forms / 2.2：
Generalizations / 2.3：
Exercises for Chapter 2
Parallel Transport, Connections, and Covariant Derivatives / 3：
Connections in Vector Bundles / 3.1：
Metric Connections. The Yang-Mills Functional / 3.2：
The Levi-Civita Connection / 3.3：
Connections for Spin Structures and the Dirac Operator / 3.4：
The Bochner Method / 3.5：
The Geometry of Submanifolds. Minimal Submanifolds / 3.6：
Exercises for Chapter 3
Geodesics and Jacobi Fields / 4：
1st and 2nd Variation of Arc Length and Energy / 4.1：
Jacobi Fields / 4.2：
Conjugate Points and Distance Minimizing Geodesics / 4.3：
Riemannian Manifolds of Constant Curvature / 4.4：
The Rauch Comparison Theorems and Other Jacobi Field Estimates / 4.5：
Geometric Applications of Jacobi Field Estimates / 4.6：
Approximate Fundamental Solutions and Representation Formulae / 4.7：
The Geometry of Manifolds of Nonpositive Sectional Curvature / 4.8：
Exercises for Chapter 4
A Short Survey on Curvature and Topology
Symmetric Spaces and Kahler Manifolds / 5：
Complex Projective Space. De nition of Kahler Manifolds / 5.1：
The Geometry of Symmetric Spaces / 5.2：
Some Results about the Structure of Symmetric Spaces / 5.3：
The Space Sl(n; R)=SO(n; R) / 5.4：
Symmetric Spaces of Noncompact Type as Examples of Nonpositively Curved Riemannian Manifolds / 5.5：
Exercises for Chapter 5
Morse Theory and Floer Homology / 6：
Preliminaries: Aims of Morse Theory / 6.1：
Compactness: The Palais-Smale Condition and the Existence of Saddle Points / 6.2：
Local Analysis: Nondegeneracy of Critical Points, Morse Lemma, Stable and Unstable Manifolds / 6.3：
Limits of Trajectories of the Gradient Flow / 6.4：
The Morse-Smale-Floer Condition: Transversality and Z2-Cohomology / 6.5：
Orientations and Z-homology / 6.6：
Homotopies / 6.7：
Graph ows / 6.8：
Orientations / 6.9：
The Morse Inequalities / 6.10：
The Palais-Smale Condition and the Existence of Closed Geodesics / 6.11：
Exercises for Chapter 6
Variational Problems from Quantum Field Theory / 7：
The Ginzburg-Landau Functional / 7.1：
The Seiberg-Witten Functional / 7.2：
Exercises for Chapter 7
Harmonic Maps / 8：
De nitions / 8.1：
Twodimensional Harmonic Mappings and Holomorphic Quadratic Di erentials / 8.2：
The Existence of Harmonic Maps in Two Dimensions / 8.3：
De nition and Lower Semicontinuity of the Energy Integral / 8.4：
Weakly Harmonic Maps. Regularity Questions / 8.5：
Higher Regularity / 8.6：
Formulae for Harmonic Maps. The Bochner Technique / 8.7：
Harmonic Maps into Manifolds of Nonpositive Sectional Curvature: Existence / 8.8：
Harmonic Maps into Manifolds of Nonpositive Sectional Curvature: Regularity / 8.9：
Harmonic Maps into Manifolds of Nonpositive Sectional Curvature: Uniqueness and Other properties / 8.10：
Exercises for Chapter 8
Linear Elliptic Partial Dierential Equation / Appendix A：
Sobolev Spaces / A.1：
Existence and Regularity Theory for Solutions of Linear Elliptic Equations / A.2：
Appendix
Fundamental Groups and Covering Spaces
Index
Foundational Material / 1：
Manifolds and Di erentiable Manifolds / 1.1：
Tangent Spaces / 1.2：
4.

図書
図書
4. Riemannian geometry and geometric analysis. 4th ed
Jürgen Jost
出版情報: Berlin : Springer, c2005  xiii, 566 p. ; 24 cm
シリーズ名: Universitext
所蔵情報: loading…
目次情報: 続きを見る
Foundational Material / 1：
Manifolds and Differentiable Manifolds / 1.1：
Tangent Spaces / 1.2：
Submanifolds / 1.3：
Riemannian Metrics / 1.4：
Vector Bundles / 1.5：
Integral Curves of Vector Fields. Lie Algebras / 1.6：
Lie Groups / 1.7：
Spin Structures / 1.8：
Exercises for Chapter 1
De Rham Cohomology and Harmonic Differential Forms / 2：
The Laplace Operator / 2.1：
Representing Cohomology Classes by Harmonic Forms / 2.2：
Generalizations / 2.3：
Exercises for Chapter 2
Parallel Transport, Connections, and Covariant Derivatives / 3：
Connections in Vector Bundles / 3.1：
Metric Connections. The Yang-Mills Functional / 3.2：
The Levi-Civita Connection / 3.3：
Connections for Spin Structures and the Dirac Operator / 3.4：
The Bochner Method / 3.5：
The Geometry of Submanifolds. Minimal Submanifolds / 3.6：
Exercises for Chapter 3
Geodesics and Jacobi Fields / 4：
1st and 2nd Variation of Arc Length and Energy / 4.1：
Jacobi Fields / 4.2：
Conjugate Points and Distance Minimizing Geodesics / 4.3：
Riemannian Manifolds of Constant Curvature / 4.4：
The Rauch Comparison Theorems and Other Jacobi Field Estimates / 4.5：
Geometric Applications of Jacobi Field Estimates / 4.6：
Approximate Fundamental Solutions and Representation Formulae / 4.7：
The Geometry of Manifolds of Nonpositive Sectional Curvature / 4.8：
Exercises for Chapter 4
A Short Survey on Curvature and Topology
Symmetric Spaces and Kähler Manifolds / 5：
Complex Projective Space / 5.1：
Kähler Manifolds / 5.2：
The Geometry of Symmetric Spaces / 5.3：
Some Results about the Structure of Symmetric Spaces / 5.4：
The Space Sl(n, <$>{\op R}<$>)/SO(n, <$>{\op R}<$>) / 5.5：
Symmetric Spaces of Noncompact Type as Examples of Nonpositively Curved Riemannian Manifolds / 5.6：
Exercises for Chapter 5
Morse Theory and Floer Homology / 6：
Preliminaries: Aims of Morse Theory / 6.1：
Compactness: The Palais-Smale Condition and the Existence of Saddle Points / 6.2：
Local Analysis: Nondegeneracy of Critical Points, Morse Lemma, Stable and Unstable Manifolds / 6.3：
Limits of Trajectories of the Gradient Flow / 6.4：
The Morse-Smale-Floer Condition: Transversality and <$>{\op Z}<$>2-Cohomology / 6.5：
Orientations and <$>{\op Z}<$>-homology / 6.6：
Homotopies / 6.7：
Graph flows / 6.8：
Orientations / 6.9：
The Morse Inequalities / 6.10：
The Palais-Smale Condition and the Existence of Closed Geodesics / 6.11：
Exercises for Chapter 6
Variational Problems from Quantum Field Theory / 7：
The Ginzburg-Landau Functional / 7.1：
The Seiberg-Witten Functional / 7.2：
Exercises for Chapter 7
Harmonic Maps / 8：
Definitions / 8.1：
Twodimensional Harmonic Mappings and Holomorphic Quadratic Differentials / 8.2：
The Existence of Harmonic Maps in Two Dimensions / 8.3：
Definition and Lower Semicontinuity of the Energy Integral / 8.4：
Weakly Harmonic Maps. Regularity Questions / 8.5：
Higher Regularity / 8.6：
Formulae for Harmonic Maps. The Bochner Technique / 8.7：
Harmonic Maps into Manifolds of Nonpositive Sectional Curvature: Existence / 8.8：
Harmonic Maps into Manifolds of Nonpositive Sectional Curvature: Regularity / 8.9：
Harmonic Maps into Manifolds of Nonpositive Sectional Curvature: Uniqueness and Other properties / 8.10：
Exercises for Chapter 8
Linear Elliptic Partial Differential Equation / Appendix A：
Sobolev Spaces / A.1：
Existence and Regularity Theory for Solutions of Linear Elliptic Equations / A.2：
Fundamental Groups and Covering Spaces / Appendix B：
Bibliography
Index
Foundational Material / 1：
Manifolds and Differentiable Manifolds / 1.1：
Tangent Spaces / 1.2：
5.

図書
図書
5. Riemannian geometry and geometric analysis. 6th ed
Jürgen Jost
出版情報: Heidelberg : Springer, c2011  xiii, 611 p. ; 24 cm
シリーズ名: Universitext
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