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

Abstract 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）.