Singularities of reflected spherical light rays from spacelike curve on the de Sitter [formula omitted]-space

Abstract

The de Sitter geometry is a model of the universe then, the examination of the geometric events on the de Sitter space is very meaningful for the universe. Also, it is very important physically to determine the trajectory followed by the reflected light rays and the singular points formed by them. The aim of this study is to examine the mirror images formed by the reflected light rays from the spacelike mirror curve on the de Sitter 3-space. The caustic shapes arising from the spacelike curve on the de Sitter 3-space are obtained and they are characterized by using the Darboux frame of the spacelike curve. Then, its singular points are obtained in terms of the Darboux frame apparatus of the mirror curve and the shapes in which they are locally diffeomorphic will be investigated.