Differential geometric structures
Useful for independent study and as a reference work, this introduction to differential geometry features many examples and exercises. It defines geometric structure by specifying the parallel transport in an appropriate fiber bundle, focusing on the simplest cases of linear parallel transport in a vector bundle. The treatment opens with an introductory chapter on fiber bundles that proceeds to examinations of connection theory for vector bundles and Riemannian vector bundles. Additional topics…
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- Full title :Differential geometric structures / Walter A. Poor, Center for Naval Analyses.
Summary
Useful for independent study and as a reference work, this introduction to differential geometry features many examples and exercises. It defines geometric structure by specifying the parallel transport in an appropriate fiber bundle, focusing on the simplest cases of linear parallel transport in a vector bundle. The treatment opens with an introductory chapter on fiber bundles that proceeds to examinations of connection theory for vector bundles and Riemannian vector bundles. Additional topics include the role of harmonic theory, geometric vector fields on Riemannian manifolds, Lie groups, symmetric spaces, and symplectic and Hermitian vector bundles. A consideration of other differential geometric structures concludes the text, including surveys of characteristic classes of principal bundles, Cartan connections, and spin structures.
Read More ↓Edition Statements
- Publication Date:©1981
- Edition:Dover edition
Publication Statements
- Publisher(s):Dover Publications
- Place of Publication:Mineola, New York
- Language:eng
- Publication Date:©1981
Notes
"This Dover edition, first published in 2007, is an unabridged, slightly corrected republication of the work originally published by McGraw Hill, Inc., New York, in 1981"--Title page verso.
The Physical Object
- Description:1 online resource (xiii, 338 pages) : : illustrations
Edition Identifiers
- ISBN:9780486151915, 0486151913
- oclc:ocn767547056
- LC Classification:QA641
- Dewey Decimal:516.3/6
Table of Contents
An introduction to fiber bundles -- Connection theory for vector bundles -- Riemannian vector bundles -- Harmonic theory -- Geometric vector fields on Riemannian manifolds -- Lie groups -- Symmetric spaces -- Symplectic and Hermitian vector bundles -- Other differential geometric structures.
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