Introduction to Smooth Manifolds

This book is an introductory graduate-level textbook on the theory of smooth manifolds. Its goal is to familiarize students with the tools they will need in order to use manifolds in mathematical or scientific research-smooth structures, tangent vectors and covectors, vector bundles, immersed and em...

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Bibliographic Details
Call Number:Libro Electrónico
Main Author: Lee, John (Author)
Corporate Author: SpringerLink (Online service)
Format: Electronic eBook
Language:Inglés
Published: New York, NY : Springer New York : Imprint: Springer, 2012.
Edition:2nd ed. 2012.
Series:Graduate Texts in Mathematics, 218
Subjects:
Geometry, Differential.
Differential Geometry.
Online Access:Texto Completo
Table of Contents:
  • Preface
  • 1 Smooth Manifolds
  • 2 Smooth Maps
  • 3 Tangent Vectors
  • 4 Submersions, Immersions, and Embeddings
  • 5 Submanifolds
  • 6 Sard's Theorem
  • 7 Lie Groups
  • 8 Vector Fields
  • 9 Integral Curves and Flows
  • 10 Vector Bundles
  • 11 The Cotangent Bundle
  • 12 Tensors
  • 13 Riemannian Metrics
  • 14 Differential Forms
  • 15 Orientations
  • 16 Integration on Manifolds.- 17 De Rham Cohomology.- 18 The de Rham Theorem
  • 19 Distributions and Foliations.- 20 The Exponential Map.- 21 Quotient Manifolds.-  22 Symplectic Manifolds
  • Appendix A: Review of Topology
  • Appendix B: Review of Linear Algebra
  • Appendix C: Review of Calculus
  • Appendix D: Review of Differential Equations
  • References
  • Notation Index
  • Subject Index.

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