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December 2005 Total curvature of noncompact piecewise Riemannian 2-polyhedra
Jin-ichi Itoh, Fumiko Ohtsuka
Tsukuba J. Math. 29(2): 471-493 (December 2005). DOI: 10.21099/tkbjm/1496164966

Abstract

In this paper, we treat piecewise Riemannian 2-polyhedra which are combinatorial 2-polyhedra such that each 2-simplex is isometric to a triangle bounded by three smooth curves on some Riemannian 2-manifold. We will introduce the total curvature $C(X)$ of a piecewise Riemannian 2-polyhedron $X$ not only in the compact case but also in the noncompact case, and obtain some generalizations of the Gauss-Bonnet theorem and the Cohn-Vossen theorem. Furthermore, we will show that the difference between $C(X)$ and some value concerning to the topology of $X$ coincides with some expanding growth rate of $X$.

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Jin-ichi Itoh. Fumiko Ohtsuka. "Total curvature of noncompact piecewise Riemannian 2-polyhedra." Tsukuba J. Math. 29 (2) 471 - 493, December 2005. https://doi.org/10.21099/tkbjm/1496164966

Information

Published: December 2005
First available in Project Euclid: 30 May 2017

zbMATH: 1104.53039
MathSciNet: MR2177022
Digital Object Identifier: 10.21099/tkbjm/1496164966

Rights: Copyright © 2005 University of Tsukuba, Institute of Mathematics

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Vol.29 • No. 2 • December 2005
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