Ricci solitons on α-Sasakian manifolds with quarter symmetric metric connection

Abstract

The main object of the present paper is to discuss about the quarter symmetric metric connection on α-Sasakian Manifold with respect to Ricci Soliton. In this paper, firstly, we discuss the quarter symmetric metric connection on α-Sasakian manifold. Secondly, we elaborate the results of quarter symmetric metric connection on α-Sasakian manifold which admits Ricci Soliton, and also flourish a non-trivial example of α-Sasakian manifold and validate some of our results. Thirdly, we classify certain curvature properties of the Ricci α-Sasakian manifold in regard to Quarter symmetric metric connection. Finally, we show Ricci Soliton on submanifold of α-Sasakian manifold in term of Levi-Civita and quarter symmetric metric connection.