Introduction to Differentiable Manifolds 9780486471723
The first book to treat manifold theory at an introductory level, this text surveys basic concepts in the modern approac
135 7 14MB
English Pages 229 Year 2009
Table of contents :
Preface vii
Chapter 1 Euclidean, Affine, and Differentiable Structure on Rⁿ 1
Chapter 2 Differentiable Manifolds 24
Chapter 3 Projective Spaces and Projective Algebraic Varieties 52
Chapter 4 The Tangent Bundle of a Differentiable Manifold 71
Chapter 5 Submanifolds and Riemann Metrics 86
Chapter 6 The Whitney Imbedding Theorem 106
Chapter 7 Lie Groups and Their One-parameter Sub-groups 117
Chapter 8 Integral Manifolds and Lie Subgroups 135
Chapter 9 Fiber Bundles 158
Chapter 10 Multilinear Algebra 186
References 213
Index 215
Preface vii
Chapter 1 Euclidean, Affine, and Differentiable Structure on Rⁿ 1
Chapter 2 Differentiable Manifolds 24
Chapter 3 Projective Spaces and Projective Algebraic Varieties 52
Chapter 4 The Tangent Bundle of a Differentiable Manifold 71
Chapter 5 Submanifolds and Riemann Metrics 86
Chapter 6 The Whitney Imbedding Theorem 106
Chapter 7 Lie Groups and Their One-parameter Sub-groups 117
Chapter 8 Integral Manifolds and Lie Subgroups 135
Chapter 9 Fiber Bundles 158
Chapter 10 Multilinear Algebra 186
References 213
Index 215
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