  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
