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2 Remote Warehouse Mathematics- Differential Geometry
1 Remote Warehouse Mathematics- Differential Geometry

Introduction to Differentiable Manifolds

by

Introduction to Differentiable Manifolds Cover

 

Synopses & Reviews

Publisher Comments:

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.  

Synopsis:

This text presents basic concepts in the modern approach to differential geometry. Topics include Euclidean spaces, submanifolds, and abstract manifolds; fundamental concepts of Lie theory; fiber bundles; and multilinear algebra. 1963 edition.

Synopsis:

The first book to treat manifold theory at an introductory level, this text presents basic concepts in the modern approach to differential geometry. The first six chapters define and illustrate differentiable manifolds. The final four chapters investigate the roles of differential structures in a variety of situations. 1963 edition.

Table of Contents

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

Product Details

ISBN:
9780486471723
Author:
Auslander, Louis
Publisher:
Dover Publications
Author:
MacKenzie, Robert E.
Author:
Mathematics
Subject:
General Mathematics
Subject:
Geometry - Differential
Subject:
Differentiable manifolds
Subject:
Mathematics-Differential Geometry
Edition Description:
Trade Paper
Series:
Dover Books on Mathematics
Publication Date:
20090231
Binding:
TRADE PAPER
Grade Level:
General/trade
Language:
English
Illustrations:
Y
Pages:
224
Dimensions:
8.25 x 5.63 in 0.57 lb

Related Subjects

History and Social Science » Politics » General
Science and Mathematics » Mathematics » Advanced
Science and Mathematics » Mathematics » Differential Geometry
Science and Mathematics » Mathematics » General
Science and Mathematics » Mathematics » Topology

Introduction to Differentiable Manifolds New Trade Paper
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$12.95 In Stock
Product details 224 pages Dover Publications - English 9780486471723 Reviews:
"Synopsis" by ,
This text presents basic concepts in the modern approach to differential geometry. Topics include Euclidean spaces, submanifolds, and abstract manifolds; fundamental concepts of Lie theory; fiber bundles; and multilinear algebra. 1963 edition.
"Synopsis" by ,
The first book to treat manifold theory at an introductory level, this text presents basic concepts in the modern approach to differential geometry. The first six chapters define and illustrate differentiable manifolds. The final four chapters investigate the roles of differential structures in a variety of situations. 1963 edition.
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