Notes on the integral geometry in the hyperbolic plane

Abstract

The Integral Geometry in the hyperbolic plane was initiated many years ago in the article “Integral Geometry on surfaces of constant negative curvature”, written by LL.A. Santaló, in 1943. Later on, it was applied to the geometry of random mosaics in the hyperbolic plane [Santaló, Ll. A. and Yanez, I., 1972]. In the present work we extend to the hyperbolic plane some new results of the Euclidean integral geometry which have been given in recent years for several authors, in particular certain results of H. Hadwiger and some formulas of H. J. Firey, R. Schneider and W. Weil on the kinematic measure for sets of support figures