Hyperbolic n-simplex and Orthogonal Projection in de Sitter n-space

摘要

In this study, we give the orthogonal projection to a k-plane of de Sitter n-space using Gram matrix of a hyperbolic n-simplex. By such projections, a point on de Sitter n-space is sent along a time-like, space-like or light-like geodesic to the point at such geodesics meet orthogonally the chosen k-plane of projection.