An elementary proof of Sforza-Santaló relation for spherical and hyperbolic polyhedra (Q2868491)

This paper relies on a previous work of the author [Bull. Korean Math. Soc. 46, No. 6, 1099--1133 (2009; Zbl 1194.51022)] on the extended hyperbolic \(n\)-space. This space arises from the Klein model of hyperbolic \(n\)-space by a natural extension of the hyperbolic (Riemannian) metric to a semi-Riemannian metric on the ambient projective \(n\)-space. This space in turn can be modelled on the \(n\)-sphere. The main results are analogues of formulas due to G.~Sforza (1906) and \textit{L. A. Santaló} [Integral geometry and geometric probability. Reading, Mass. etc.: Addison-Wesley Publishing Company (1976; Zbl 0342.53049)] for the hyperbolic space.