Ricci soliton on the tangent bundle with semi-symmetric metric connection

Abstract

In this paper, we studied the tangent bundle endowed with a semi-symmetric metric connection obtained by vertical and complete lifts of a semi-symmetric metric P-connection on the base manifold. Firstly, we give a relationship between (TM; g^c) and (M; g) to be an Einstein manifold. Secondly, we investigate necessary and suffcient conditions for (TM; g^c) with a complete and vertical lift of torqued potential fields to be Ricci soliton.