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Differential Geometry: Manifolds, Curves, and Surfaces : Manifolds, Curves, and Surfaces - Marcel Berger

Differential Geometry: Manifolds, Curves, and Surfaces

Manifolds, Curves, and Surfaces

Hardcover

Published: 1st November 1987
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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.

Background
Differential Equations
Differentiable Manifolds
Partitions of Unity, Densities and Curves
Critical Points
Differential Forms
Integration of Differential Forms
Degree Theory
Curves: The Local Theory
Plane Curves: The Global Theory
A Guide to the Local Theory of Surfaces in R3
A Guide to the Global Theory of Surfaces
Bibliography
Index of Symbols and Notations
Index
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780387966267
ISBN-10: 0387966269
Series: Graduate Texts In Mathematics
Audience: General
Format: Hardcover
Language: English
Number Of Pages: 476
Published: 1st November 1987
Publisher: Springer-Verlag New York Inc.
Country of Publication: US
Dimensions (cm): 24.13 x 17.15  x 3.18
Weight (kg): 0.86