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Differential Geometry: Manifolds, Curves, and Surfaces /

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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 cur...

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Bibliographic Details
Main Author: Berger, Marcel
Corporate Author: SpringerLink (Online service)
Other Authors: Gostiaux, Bernard
Format: eBook
Language:English
Published: New York, NY : Springer New York, 1988.
Series:Graduate texts in mathematics ; 115.
Subjects:
Mathematics.
Global differential geometry.
Electronic books.
Online Access:Connect to the full text of this electronic book
Table of Contents:
  • 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.