On the semi-symmetric Lorentzian spaces

TL;DR

This paper explores properties of semi-symmetric Lorentzian manifolds, focusing on their foliation structure and the real eigenvalues of the Ricci operator in the Lorentzian setting.

Contribution

It provides new insights into the geometric structure of semi-symmetric Lorentzian manifolds, particularly regarding their foliation and Ricci operator eigenvalues.

Findings

Semi-symmetric Lorentzian manifolds are foliated.

Ricci operator has only real eigenvalues in these manifolds.

Properties of semi-symmetric pseudo-Riemannian manifolds are characterized.

Abstract

We give some properties of semi-symmetric pseudo-Riemannian manifolds. These are foliated manifolds and for the Lorentzian metric, the Ricci operator has only real eigenvalues.