Differential Geometric Structures
Walter A. Poor
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.
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.
კატეგორია:
წელი:
2007
გამომცემლობა:
Dover Publications
ენა:
english
გვერდები:
352
ISBN 10:
048645844X
ISBN 13:
9780486458441
სერია:
Dover Books on Mathematics
ფაილი:
PDF, 19.99 MB
IPFS:
,
english, 2007
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