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
131 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
![An Introduction to Differentiable Manifolds and Riemannian Geometry [2 ed.]
0121160521, 9780121160524, 9780080874395](https://ebin.pub/img/200x200/an-introduction-to-differentiable-manifolds-and-riemannian-geometry-2nbsped-0121160521-9780121160524-9780080874395.jpg)
![Introduction to smooth manifolds [2nd ed]
9781441999818, 9781441999825, 1441999817, 1441999825](https://ebin.pub/img/200x200/introduction-to-smooth-manifolds-2nd-ed-9781441999818-9781441999825-1441999817-1441999825.jpg)
![Differentiable Manifolds: Forms, Currents, Harmonic Forms (Grundlehren der mathematischen Wissenschaften) [1 ed.]
3540134638, 9783540134633](https://ebin.pub/img/200x200/differentiable-manifolds-forms-currents-harmonic-forms-grundlehren-der-mathematischen-wissenschaften-1nbsped-3540134638-9783540134633.jpg)
![Differentiable Dynamical Systems: An Introduction to Structural Stability and Hyperbolicity [1 ed.]
1470427990, 9781470427993](https://ebin.pub/img/200x200/differentiable-dynamical-systems-an-introduction-to-structural-stability-and-hyperbolicity-1nbsped-1470427990-9781470427993.jpg)