Another Geometric Realization of Relativity: The Anti-de Sitter Space–Time

There are a lot of similarities between de Sitter and Anti-de Sitter space–times; therefore, we want to present here some geometric aspects which are not highlighted in the previous chapter. Before developing a geometric theory of gravity which can be extended in Minkowski \(M^{(p,q)}\) spaces and before reaching the subject of Anti-de Sitter space–times as examples of universes without matter, we want to introduce some facts related to the centro-affine geometry, a branch of geometry developed by Gheorghe Tzitzeica. These facts are essential for the development of the chapter (see [30]).