Ricci soliton on the tangent bundle with semi-symmetric metric connection
Keywords:Ricci soliton, semi-symmetric connection, tangent bundle, potential field, Einstein manifold
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; gc) and (M; g) to be an Einstein manifold. Secondly, we investigate necessary and suffcient conditions for (TM; gc) with a complete and vertical lift of torqued potential fields to be Ricci soliton.