Quasielliptic, Quasihyperbolic, and Quasi-Euclidean Geometries

Abstract

Since the Euclidean space R n and pseudo-Euclidean space R l n can be defined as the projective space P n with a distinguished hyperplane in which the absolute hyperquadrics of the spaces S n-1 or S l n-1 are given, there are spaces corresponding them by the duality principle of P n . These dual spaces are called co-Euclidean, respectively copseudo-Euclidean, spaces and are denoted by R n* , respectively R l n* .