Introduction to Differentiable Manifolds

Auslander, Louis; MacKenzie, Robert E.

ISBN 10: 0486471721 / ISBN 13: 9780486471723

Editore: Dover Publications, 2009

May have limited writing in cover pages. Pages are unmarked. ~ ThriftBooks: Read More, Spend Less. Codice articolo G0486471721I4N00

Riassunto:

The first book to treat manifold theory at an introductory level, this text surveys basic concepts in the modern approach to differential geometry. The first six chapters define and illustrate differentiable manifolds, and the final four chapters investigate the roles of differential structures in a variety of situations.
Starting with an introduction to differentiable manifolds and their tangent spaces, the text examines Euclidean spaces, their submanifolds, and abstract manifolds. Succeeding chapters explore the tangent bundle and vector fields and discuss their association with ordinary differential equations. The authors offer a coherent treatment of the fundamental concepts of Lie group theory, and they present a proof of the basic theorem relating Lie subalgebras to Lie subgroups. Additional topics include fiber bundles and multilinear algebra. An excellent source of examples and exercises, this graduate-level text requires a solid understanding of the basic theory of finite-dimensional vector spaces and their linear transformations, point-set topology, and advanced calculus.

Contenuti: Chapter 1. Euclidean, Affine, and Differentiable Structure on Rn Chapter 2. Differentiable Manifolds Chapter 3. Projective Spaces and Projective Algebraic Varieties Chapter 4. The Tangent Bundle of a Differentiable Manifold Chapter 5. Submanifolds and Riemann Metrics Chapter 6. The Whitney Imbedding Theorem Chapter 7. Lie Groups and Their One-parameter Sub-groups Chapter 8. Integral Manifolds and Lie Subgroups Chapter 9. Fiber Bundles Chapter 10. Multilinear Algebra References Index

Dati bibliografici

Titolo: Introduction to Differentiable Manifolds
Casa editrice: Dover Publications
Data di pubblicazione: 2009
Legatura: Paperback
Condizione: Very Good
Condizione sovraccoperta: No Jacket