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黎曼几何和几何分析 第6版 by (德)约斯特(Jurgen Jost)著, 约斯特 (Jost, Jurgen), Jurgen Jost著, 约斯特 is a book available to read on EtoBox.

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1 (p1): 1 Riemannian Manifolds 1 (p1-1): 1.1 Manifolds and Differentiable Manifolds 6 (p1-2): 1.2 Tangent Spaces 10 (p1-3): 1.3 Submanifolds 13 (p1-4): 1.4 Riemannian Metrics 28 (p1-5): 1.5 Existence of Geodesics on Compact Manifolds 31 (p1-6): 1.6 The Heat Flow and the Existence of Geodesics 35 (p1-7): 1.7 Existence of Geodesics on Complete Manifolds 37 (p1-8): Exercises for Chapter 1 41 (p2): 2 Lie Groups and Vector Bundles 41 (p2-1): 2.1 Vector Bundles 51 (p2-2): 2.2 Integral Curves of Vector Fields.Lie Algebras 61 (p2-3): 2.3 Lie Groups 67 (p2-4): 2.4 Spin Structures 87 (p2-5): Exercises for Chapter 2 89 (p3): 3 The Laplace Operator and Harmonic Differential Forms 89 (p3-1): 3.1 The Laplace Operator on Functions 94 (p3-2): 3.2 The Spectrum of the Laplace Operator 102 (p3-3): 3.3 The Laplace Operator on Forms 113 (p3-4): 3.4 Representing Cohomology Classes by Harmonic Forms 122 (p3-5): 3.5 Generalizations 123 (p3-6): 3.6 The Heat Flow and Harmonic Forms 129 (p3-7): Exercises for Chapter 3 133 (p4): 4 Connections and Curvature 133 (p4-1): 4.1 Connections in Vector Bundles 144 (p4-2): 4.2 Metric Connections.The Yang-Mills Functional 160 (p4-3): 4.3 The Levi-Civita Connection 175 (

Author

(德)约斯特(Jurgen Jost)著, 约斯特 (Jost, Jurgen), Jurgen Jost著, 约斯特

Publisher

北京/西安:世界图书出版公司

Published

2015

Language

ZH

ISBN

9787510084447