JP Journal of Geometry and Topology
Volume 11, Issue 1, Pages 65 - 76
(March 2011)
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TWO COUNTEREXAMPLES OF GLOBAL DIFFERENTIAL GEOMETRY FOR POLYHEDRA
Abdênago Barros, Esdras Medeiros and Romildo Silva
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Abstract:
In this article, we show, by giving counterexamples, that two classical results of global differential geometry are not valid for polyhedral surfaces. Considering the set of compact smooth surfaces, we exhibit counterexamples concerning the Cohn-Vossen theorem and the existence of elliptical points. The key point on the construction of such polyhedral surfaces is the application of a nice discrete version of the Gaussian curvature. |
| Keywords and phrases: Gauss-Bonnet, Cohn-Vossen, polyhedra, discrete curvature. |
| Communicated by Yasuo Matsushita |
| Number of Downloads: 302 | Number of Views: 988 |
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