Abstract

In this paper we prove a Schläfli differential formula for the volume of simplices in central unit hyperquadrics of semi-Euclidean space R_qⁿ⁺¹. Then we apply this result to obtain Gauss-Bonnet formulas for simplices with riemannian faces in the de Sitter sphere, and to generalize a formula of L. Santaló relating the volume of a hyperbolic simplex with the measure of the set of hyperbolic hyperplanes intersecting it.

Authors