Differential Geometric Structures (Dover Books on Mathematics) - Softcover

Walter A. Poor

Softcover

ISBN 10: 048645844X ISBN 13: 9780486458441

Publisher: Dover, 2007

Synopsis

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.

Edition details

• Publisher: Dover
• Publication date: 2007
• Language: English
• ISBN 10: 048645844X
• ISBN 13: 9780486458441
• Binding: Paperback
• Number of pages: 352