Metric Structures in Differential Geometry

By:

Gerard Walschap

Format:

Paperback / softback

Series:

Graduate Texts in Mathematics,

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Description

This text is an elementary introduction to differential geometry. Although it was written for a graduate-level audience, the only requisite is a solid back ground in calculus, linear algebra, and basic point-set topology. The first chapter covers the fundamentals of differentiable manifolds that are the bread and butter of differential geometry. All the usual topics are cov ered, culminating in Stokes' theorem together with some applications. The stu dents' first contact with the subject can be overwhelming because of the wealth of abstract definitions involved, so examples have been stressed throughout. One concept, for instance, that students often find confusing is the definition of tangent vectors. They are first told that these are derivations on certain equiv alence classes of functions, but later that the tangent space of ffi.n is "the same" n as ffi. . We have tried to keep these spaces separate and to carefully explain how a vector space E is canonically isomorphic to its tangent space at a point. This subtle distinction becomes essential when later discussing the vertical bundle of a given vector bundle.

Release date Australia

November 29th, 2010

Author

Gerard Walschap

Audience

Professional & Vocational

Edition

Softcover reprint of the original 1st ed. 2004

Illustrations

7 Illustrations, black and white; VIII, 229 p. 7 illus.

Pages

229

Series

Graduate Texts in Mathematics,

Dimensions

156x234x12

ISBN-13

9781441919137

Product ID

8938597

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Metric Structures in Differential Geometry

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