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Indian Journal of Pure and Applied Mathematics

, Volume 46, Issue 6, pp 893–900 | Cite as

The Gauss-Bonnet theorem

  • M. S. Raghunathan
Article

Abstract

In this note we give a proof of the Gauss-Bonnet theorem for Riemannian manifolds (of any dimension) using Morse theory.

Key words

Chern Weil theory Euler characteristic 

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References

  1. 1.
    Shiing-Shen Chern, On the curvature integral in Riemannian manifold, Annals of Mathematics, 46 (1945), 674–684.zbMATHMathSciNetCrossRefGoogle Scholar
  2. 2.
    John Milnor, Morse Theory, Princeton University Press, Princeton (1963).zbMATHGoogle Scholar
  3. 3.
    Shigeyki Morita, Geometry of Differential Forms, Translations of Mathematical Monographs, American Mathematical Society, Vol. 201, (2001).Google Scholar
  4. 4.
    Wei-Ping Zhang, Lectures on Chern-Weil Theory and Witten Deformations, World Scientific, (2002).Google Scholar

Copyright information

© The Indian National Science Academy 2015

Authors and Affiliations

  1. 1.National Centre for MathematicsIndian Institute of TechnologyMumbaiIndia

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