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Angular Measure and Integral Curvature

Published online by Cambridge University Press:  20 November 2018

Herbert Busemann
Herbert Busemann*
Affiliation:
University of Southern California
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The Gauss-Bonnet Theorem leads through well known arguments to the fact that the integral curvature of a two-dimensional closed orientable manifold M of genus p equals 4π(1 — p). This implies, for instance, that the Gauss curvature K can neither be everywhere positive nor everywhere negative, if M is homeomorphic to a torus.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 1 , Issue 3 , 01 June 1949 , pp. 279 - 296
Copyright
Copyright © Canadian Mathematical Society 1949

References

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