Bochner’s method for cell complexes and combinatorial Ricci curvature. (English) Zbl 1040.53040

An original notion of combinatorial scalar curvature of cells in a cell complex is proposed. Properties of the Ricci curvature of a cell complex are studied and compared with corresponding properties of Riemannian manifolds. An analogue of the classical Bochner theorem about topological characteristics of a cell complex with positive combinatorial curvature is proved.


53C20 Global Riemannian geometry, including pinching
53C45 Global surface theory (convex surfaces à la A. D. Aleksandrov)
52B70 Polyhedral manifolds
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