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

Manifold Bonnet 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

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

Personalised recommendations