Combinatorial Ricci curvature on cell-complex and Gauss-Bonnnet Theorem
Combinatorics
2017-07-12 v2 Differential Geometry
Abstract
In this paper we present the Ricci curvature on cell-complexes and show the Gauss-Bonnnet type theorem on graphs and 2-complex that decomposes closed surface. The defferential forms on a cell complex is defined as linear maps on chain complex, and Laplacian operates this defferential forms. Then we construct the Bochner-Weitzenb\"ock formula and define the Ricci curvature. This curvature is determined by the combinatorial calculation. We show also the properties of combinatorial vector fields on a cell complex
Keywords
Cite
@article{arxiv.1703.08409,
title = {Combinatorial Ricci curvature on cell-complex and Gauss-Bonnnet Theorem},
author = {Kazuyoshi Watanabe},
journal= {arXiv preprint arXiv:1703.08409},
year = {2017}
}