Some geometrical properties of 4D homogeneous pseudo-Riemannian space with trivial isotropy

Abstract

In this paper, we first consider $4D$ conformally flat homogeneous pseudo-Riemannian space with trivial isotropy, then, we investigate some geometrical properties such as being Ricci solitons and Walker on the spaces under consideration. Indeed, we give a complete classification of the cases giving rise to conformally flat homogeneous Ricci solitons or Walker spaces with trivial isotropy.

Keywords

• homogeneous atmosphere
• quasi-rhyme
• ritchie operator