On certain isometric representations for multidimensional spaces of constant curvature

Abstract

Multidimensional spaces of constant finite curvature are considered as hypersurfaces in the pseudo-Euclidean space of one dimension higher with arbitrary signature. A series of isometric representations including the projective ones, obtainable by means of generalized stereographic projection, Cayley transformation and Klein projection, are given. In the case of the projective Klein model it is shown that the spaces under consideration may be represented both in a standard form of pseudoball interiority and in the form of exteriority of the respective pseudoball.