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Integration on Manifolds

  • Klaus Jänich
Part of the Undergraduate Texts in Mathematics book series (UTM)

Abstract

Integration over n-dimensional manifolds reduces through charts to integration in ℝ n . The objects integrated on oriented manifolds are n-forms, for the following reason. For an ordinary function f : M → ℝ, the contribution of a chart domain U to the integral would clearly depend on the choice of chart h But for an n-form, the integral of its component function pulled down by an orientation-preserving chart is independent of the coordinates, as we see from the changeof-variables formula for multiple integrals in ℝ n . This is the main content of Chapter 5. Section 5.4 contains the technical details and Section 5.3 a summary of necessary background. In the first two sections we give an intuitive view of integration on manifolds.

Keywords

Measure Zero Measurable Subset Oriented Manifold Intuitive View Arbitrary Measure Space 
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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Copyright information

© Springer Science+Business Media New York 2001

Authors and Affiliations

  • Klaus Jänich
    • 1
  1. 1.NWF-I MathematikUniversität RegensburgRegensburgGermany

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