Torse-forming vector fields and normalized null hypersurfaces

Abstract

The study focuses on normalized null hypersurfaces within semi-Riemannian manifolds that possess torse-forming vector fields. We demonstrate that these hypersurfaces exhibit a triple product structure. Additionally, we present obstruction results related to both topology and specific geometric criteria concerning the rigging and rigged vector field. We also provide a result on the splitting of the hypersurface, which is endowed with its rigged Riemannian structure. Furthermore, taking the potential vector field as the screen component of a torse-forming vector field, we investigate screen distribution with Ricci solitons.