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Applications of Stokes’ Theorem

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Part of the Graduate Texts in Mathematics book series (GTM,volume 160)

Abstract

In this chapter we give a survey of applications of Stokes’ theorem, concerning many situations. Some come just from the differential theory, such as the computation of the maximal de Rham cohomology (the space of all forms of maximal degree modulo the subspace of exact forms); some come from Riemannian geometry; and some come from complex manifolds, as in Cauchy’s theorem and the Poincaré residue theorem. I hope that the selection of topics will give readers an outlook conducive for further expansion of perspectives. The sections of this chapter are logically independent of each other, so the reader can pick and choose according to taste or need.

Keywords

  • Riemannian Manifold
  • Compact Support
  • Differential Form
  • Volume Form
  • Regular Point

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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© 1995 Springer-Verlag New York, Inc.

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Lang, S. (1995). Applications of Stokes’ Theorem. In: Lang, S. (eds) Differential and Riemannian Manifolds. Graduate Texts in Mathematics, vol 160. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-4182-9_13

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  • DOI: https://doi.org/10.1007/978-1-4612-4182-9_13

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4612-8688-2

  • Online ISBN: 978-1-4612-4182-9

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