Differential Forms and Applications

Released on by Manfredo P. Do Carmo
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  • Differential Forms and Applications Book Detail

  • Author : Manfredo P. Do Carmo
  • Release Date : 2012-12-06
  • Publisher : Springer Science & Business Media
  • Genre : Mathematics
  • Pages : 124
  • ISBN 13 : 3642579515
  • File Size : 15,15 MB
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Differential Forms and Applications by Manfredo P. Do Carmo PDF Summary

Book Description: An application of differential forms for the study of some local and global aspects of the differential geometry of surfaces. Differential forms are introduced in a simple way that will make them attractive to "users" of mathematics. A brief and elementary introduction to differentiable manifolds is given so that the main theorem, namely Stokes' theorem, can be presented in its natural setting. The applications consist in developing the method of moving frames expounded by E. Cartan to study the local differential geometry of immersed surfaces in R3 as well as the intrinsic geometry of surfaces. This is then collated in the last chapter to present Chern's proof of the Gauss-Bonnet theorem for compact surfaces.

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