The Gaussian curvature of Alexandrov surfaces

Abstract

We generalize the Gauss-Bonnet theorem for Alexandrov surfaces and show that we can define the Gaussian curvature almost everywhere on an Alexandrov surface.\S 0. Introduction.A classical theorem in the theory of surfaces states that if $\Delta$ is a sufficiently small geodesic triangle bounding a disk on a smooth Riemannian 2-manifold $M$ , and if $A,$ $B$ and $C$ are the inner angles of $\Delta$ , then (0.1)$\int_{\Delta}GdM=A+B+C-\pi$ ,

Locations

• Journal of the Mathematical Society of Japan - View - PDF