INTRODUCTION TO DIFFERENTIABLE MANIFOLDS

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ISBN: 9780486471723
Author/Editor: AUSLANDER LOUIS ET.AL

Publisher: DOVER

Year: 2009

1 in stock (can be backordered)

SKU: ABD-DOV-4083 Category:

Description

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.”

Additional information

Weight 0.25 kg

Product Properties

Year of Publication

2009

Table of Contents

Chapter 1. Euclidean, Affine, and Differentiable Structure on RnChapter 2. Differentiable ManifoldsChapter 3. Projective Spaces and Projective Algebraic VarietiesChapter 4. The Tangent Bundle of a Differentiable ManifoldChapter 5. Submanifolds and Riemann MetricsChapter 6. The Whitney Imbedding TheoremChapter 7. Lie Groups and Their One-parameter Sub-groupsChapter 8. Integral Manifolds and Lie SubgroupsChapter 9. Fiber BundlesChapter 10. Multilinear AlgebraReferencesIndex

Author

AUSLANDER LOUIS ET.AL

ISBN/ISSN

9780486471723

Binding

n/a

Edition

1

Publisher

DOVER

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