Orthogonal Projections Based on Hyperbolic and Sphericaln-Simplex

Abstract

Orthogonal projection along a geodesic to the chosenk-plane is introduced using edge and Gram matrix of ann-simplex in hyperbolic or sphericaln-space. The distance from a point tok-plane is obtained by the orthogonal projection. It is also given the perpendicular foot from a point tok-plane of hyperbolic and sphericaln-space.