Characterizations of Ricci Almost Solitons on Lorentzian Manifolds

Abstract

The focus of this paper is to investigate Ricci almost solitons on Lorentzian manifolds with special metric connection, called semi-symmetric metric u-connection. First, we prove that any quasi-Einstein Lorentzian manifold admitting semisymmetric metric u-connection, whose metric is Ricci soliton, is an Einstein manifold. Similar conclusion also holds for a Lorentzian manifold equipped semi-symmetric metric u-connection admitting Ricci soliton whose soliton vector Z parallel to the vector u. Finally, we study gradient Ricci almost soliton on Lorentzian manifold with semi-symmetric metric u-connection. Keywords: Lorentzian manifolds, symmetric spaces, semi-symmetric metric connection, Ricci soliton, Gradient Ricci almost soliton

Keywords: Lorentzian manifolds, symmetric spaces, semi-symmetric metric connection, Ricci soliton, Gradient Ricci almost soliton