Lorentzian manifolds: A characterization with a type of semi-symmetric non-metric connection

Abstract

This paper characterizes the Lorentzian manifolds endowed with a semi-symmetric non-metric [Formula: see text]-connection (briefly, [Formula: see text]). First, the existence of semi-symmetric non-metric connection ([Formula: see text]) on Lorentzian manifold is established, and it is shown that an [Formula: see text]-dimensional Lorentzian manifold equipped with an [Formula: see text] is a generalized Robertson–Walker spacetime. We also establish the condition for a Lorentzian manifold together with an [Formula: see text] to be a Robertson–Walker spacetime. In this series, the properties of Ricci semi-symmetric Lorentzian manifold endowed with an [Formula: see text], almost Ricci solitons and gradient Ricci solitons are explored. Finally, a non-trivial example of Lorentzian manifold admits an [Formula: see text], which is constructed to verify some of our results.