Differential Geometric Structures

Nonfiction, Science & Nature, Mathematics, Geometry
Cover of the book Differential Geometric Structures by Walter A. Poor, Dover Publications
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Author: Walter A. Poor ISBN: 9780486151915
Publisher: Dover Publications Publication: April 27, 2015
Imprint: Dover Publications Language: English
Author: Walter A. Poor
ISBN: 9780486151915
Publisher: Dover Publications
Publication: April 27, 2015
Imprint: Dover Publications
Language: English

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.

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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.

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