Differential Geometry : Manifolds, Curves, and Surfaces
Manifolds, Curves, and Surfaces
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Publication
2012 - Springer New York
Language
English
Word Count
119,000 words, Guess
Page Count
476 pages
Identifiers
- Open LibraryOL37158576M
- ISBN-139781461269922
Classifications
- LCCQA641-670
Description
This book is an introduction to modern differential geometry. The authors begin with the necessary tools from analysis and topology, including Sard's theorem, de Rham cohomology, calculus on manifolds, and a degree theory. The general theory is illustrated and expanded using the examples of curves and surfaces. In particular, the book contains the classical local and global theory of surfaces, including the fundamental forms, curvature, the Gauss-Bonnet formula, geodesics, and minimal surfaces.
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