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Geometry VI pp 223-237 | Cite as

Some Special Tensors

  • M. M. Postnikov
Part of the Encyclopaedia of Mathematical Sciences book series (EMS, volume 91)

Abstract

The Gauss—Bonnet theorem in the previous chapter directly implies that the total curvature
$$\iint {_x}Kd\sigma $$
(1)
of a surface χ does not depend on the choice of a Riemannian metric on χ (it is the same for all metrics).

Keywords

Euler Characteristic Ricci Tensor Weyl Tensor Riemannian Space Euler Number 
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 2001

Authors and Affiliations

  • M. M. Postnikov
    • 1
  1. 1.MIRANMoscowRussia

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