Higher transgressions of the Pfaffian

• Autores: Sergiu Moroianu
• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 38, Nº 5, 2022, págs. 1425-1452
• Idioma: inglés
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• Resumen

  • 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, very much 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