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Harmonic Forms

  • Georges de Rham
Part of the Grundlehren der mathematischen Wissenschaften book series (GL, volume 266)

Abstract

We call a Riemannian space1 a differentiable manifold V endowed with a twice covariant tensor g ij such that the differential quadratic form
$$d{s^2} = \sum\limits_{i,j} {{g_{ij}}d{x^i}d{x^j}}$$
is always positive definite. In the following, we will always suppose that V is C and the given tensor g ij is C.

Keywords

Compact Space Riemannian Space Harmonic Form Geodesic Line Geodesic Sphere 
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-Verlag Berlin Heidelberg 1984

Authors and Affiliations

  • Georges de Rham
    • 1
  1. 1.LausanneSwitzerland

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