On the Volume Formulas of Cones and Orthogonal Multi-cones in S~n(1) and H~n(-1)

摘要

In the study of n-dimensional spherical or hyperbolic geometry, n ≥ 3, the volume of various objects such as simplexes, convex polytopes, etc. often becomes rather difficult to deal with. In this paper, we use the method of infinitesimal symmetrization to provide a systematic way of obtaining volume formulas of cones and orthogonal multiple cones in S~n(1) and H~n(-1).