| Differential Geometry: Manifolds, Curves, and Surfaces: Manifolds, Curves, and Surfaces 1988 Edition Contributor(s): Berger, Marcel (Author), Levy, Silvio (Translator), Gostiaux, Bernard (Author) |
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ISBN: 0387966269 ISBN-13: 9780387966267 Publisher: Springer OUR PRICE: $94.99 Product Type: Hardcover - Other Formats Published: November 1987 Annotation: 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. |
| Additional Information |
| BISAC Categories: - Mathematics | Geometry - Differential |
| Dewey: 516.36 |
| LCCN: 87027507 |
| Series: Mathematical Sciences Research Institute Publications |
| Physical Information: 1.06" H x 6.14" W x 9.21" (1.90 lbs) 476 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: This book consists of two parts, different in form but similar in spirit. The first, which comprises chapters 0 through 9, is a revised and somewhat enlarged version of the 1972 book Geometrie Differentielle. The second part, chapters 10 and 11, is an attempt to remedy the notorious absence in the original book of any treatment of surfaces in three-space, an omission all the more unforgivable in that surfaces are some of the most common geometrical objects, not only in mathematics but in many branches of physics. Geometrie Differentielle was based on a course I taught in Paris in 1969- 70 and again in 1970-71. In designing this course I was decisively influ- enced by a conversation with Serge Lang, and I let myself be guided by three general ideas. First, to avoid making the statement and proof of Stokes' formula the climax of the course and running out of time before any of its applications could be discussed. Second, to illustrate each new notion with non-trivial examples, as soon as possible after its introduc- tion. And finally, to familiarize geometry-oriented students with analysis and analysis-oriented students with geometry, at least in what concerns manifolds. |