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Index
Cover image
Title page
Table of Contents
Copyright
Preface
Errata for Volume 1 and Volume 2
Volume 1 (Cont’d)
Volume 2
List of Notation
Chapter 1: Differential Calculus
Chapter 2: Differential and Analytic Manifolds
Chapter 3: Fiber Bundles
Chapter 4: Tensor Calculus on Manifolds
Chapter 5: Differential and Integral Calculus on Manifolds
Chapter 6: Analysis on Lie Groups
Chapter 7: Connections
1: Differential Calculus
Abstract
1.1 Introduction
1.2 Fréchet differential calculus
1.3 Other approaches to differential calculus
1.4 Smooth partitions of unity
1.5 Ordinary differential equations
2: Differential and Analytic Manifolds
Abstract
2.1 Introduction
2.2 Manifolds: tangent space of a manifold at a point
2.3 Tangent linear mappings; submanifolds
2.4 Lie groups and their actions
3: Fiber Bundles
Abstract
3.1 Introduction
3.2 Tangent bundle and cotangent bundle
3.3 Fibrations
3.4 Vector bundles
3.5 Principal bundles
4: Tensor Calculus on Manifolds
Abstract
4.1 Introduction
4.2 Tensor calculus
4.3 Tensor fields
4.4 Differential forms
4.5 Pseudo-Riemannian manifolds
5: Differential and Integral Calculus on Manifolds
Abstract
5.1 Introduction
5.2 Currents and differential operators
5.3 Manifolds of mappings
5.4 Lie derivatives
5.5 Exterior differential
5.6 Stokes’ formula and applications
5.7 Integral curves and manifolds
6: Analysis on Lie Groups
Abstract
6.1 Introduction
6.2 Convolution
6.3 Classification of Lie algebras
6.4 Relation between Lie groups and Lie algebras
6.5 Harmonic analysis
7: Connections
Abstract
7.1 Introduction
7.2 Linear connections
7.3 Method of moving frames
7.4 Riemannian geometry
References
Cited Authors
Index
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