2020/11/12 by Sergiu Moroianu, Moroianu, Sergiu
Mathematics · #53 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #History and Theory of Mathematics #Mathematics and Applications
paper · pdf · doi:10.48550/arxiv.2011.06538
openalex publication_date 2020/11/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We define transgressions of arbitrary order, with respect to families of unit-vector fields indexed by a polytope, for the Pfaffian of metric connections for semi-Riemannian metrics on vector bundles. We apply this formula to compute the Euler characteristic of a Riemannian polyhedral manifold in the spirit of Chern's differential-geometric proof of the generalized Gauss-Bonnet formula on closed manifolds and on manifolds-with-boundary. As a consequence, we derive an identity for spherical and hyperbolic polyhedra linking the volumes of faces of even codimension and the measures of outer angles.