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Differential Forms

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

Abstract

On a manifold, we obtain differential forms of degree 1 as sums of the products of a function g by the differential df of another function f,
$$\sum {gdf.}$$
Expressing this in terms of the local coordinates x1,,x n , the above differential form reduces to the expression
$$\sum\limits_{i = 1}^n {{a_i}} d{x^i}\;with\;{a_i} = \sum {g\frac{{\partial f}}{{\partial {x^i}}}} .$$
If we change the local coordinate system, the coefficients a i transform as the components of a covector.

Keywords

Differential Form Local Coordinate System Inverse Image Infinite Chain Exterior Product 
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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