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

Forman, Robin

Discrete Comput. Geom. 29, No. 3, 323-374 (2003).

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.

Reviewer: Anatoliy Milka (Kharkov)

MSC:

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

Keywords:

cell complex; combinatorial Ricci curvature; Bochner theorem