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2019 Combinatorial Ricci curvature on cell-complex and Gauss-Bonnnet theorem
Kazuyoshi Watanabe
Tohoku Math. J. (2) 71(4): 533-547 (2019). DOI: 10.2748/tmj/1576724792

Abstract

In this paper, we introduce a new definition of the Ricci curvature on cell-complexes and prove the Gauss-Bonnnet type theorem for graphs and 2-complexes that decompose closed surfaces. The differential forms on a cell complex are defined as linear maps on the chain complex, and the Laplacian operates this differential forms. Our Ricci curvature is defined by the combinatorial Bochner-Weitzenböck formula. We prove some propositionerties of combinatorial vector fields on a cell complex.

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Kazuyoshi Watanabe. "Combinatorial Ricci curvature on cell-complex and Gauss-Bonnnet theorem." Tohoku Math. J. (2) 71 (4) 533 - 547, 2019. https://doi.org/10.2748/tmj/1576724792

Information

Published: 2019
First available in Project Euclid: 19 December 2019

zbMATH: 07199978
MathSciNet: MR4043924
Digital Object Identifier: 10.2748/tmj/1576724792

Subjects:
Primary: 05E45
Secondary: 53B21

Rights: Copyright © 2019 Tohoku University

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Vol.71 • No. 4 • 2019
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