微分几何初步(英文版) mobi 下载 网盘 caj lrf pdf txt 阿里云

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1 Basic Objects and Notation

1.1 Sets

1.2 Functi***

2 Linear Algebra Essentials

2.1 Vector Spaces

2.2 Subspaces

2.3 C***tructing Subspaces I: Spanning Sets

2.4 Linear Independence, Basis, and Dimension

2.5 Linear Transformati***

2.6 C***tructing Linear Transformati***

2.7 C***tructing Subspaces II: Subspaces and Linear Transformati***

2.8 The Dual of a Vector Space, Forms, and Pullbacks

2.9 Geometric Structures I: Inner Products

2.10 Geometric Structures II" Linear Symplectic Forms

2.11 For Further Reading

2.12 Exercises

3 Advanced Calculus

3.1 The Derivative and Linear Approximation

3.2 The Tangent Space I" A Geometric Definition

3.3 Geometric Sets and Subspaces of Tp(Rn)

3.4 The Tangent Space II: An Analytic Definition

3.5 The Derivative as a Linear Map Between Tangent Spaces

3.6 Diffeomorphisms

3.7 Vector Fields: From Local to Global

3.8 Integral Curves

3.9 Diffeomorphisms Generated by Vector Fields

3.10 ForFurther Reading

3.11 Exercises

4 Differential Forms and Tensors

4.1 The Algebra of Alternating Linear Forms

4.2 Operati*** on Linear Forms

4.3 Differential Forms

4.4 Operati*** on Differential Forms

4.5 Integrating Differential Forms

4.6 Tensors

4.7 The Lie Derivative

4.8 For Further Reading

4.9 Exercises

5 Rlemannlan Geometry

5.1 Basic Concepts

5.2 C***tructing Metrics; Metrics on Geometric Sets

5.3 The Riemannian Connection

5.4 Parallelism and Geodesics

5.5 Curvature

5.6 Isometrics

5.7 For Further Reading

5.8 Exercises

6 Contact Geometry

6.1 Motivation I: Huygens' Principle and Contact Elements ...

6.2 Motivation II: Differential Equati*** and Contact Elements

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