Complete lifts from a Sasakian manifold concerning the quarter symmetric metric connection to its tangent bundle

The present paper aims to study the complete lifts of the quarter symmetric metric connection and we establish the interrelation between a Levi-Civita connection and a quarter symmetric metric connection on a Sasakian manifold to its tangent bundle. The curvature and the Ricci tensors are formulated in the form of lifts concerning the quarter symmetric metric connection on a Sasakian manifold to its tangent bundle. The symmetric property of the Ricci tensor on the tangent bundle is deduced. Finally, we establish necessary and sufficient conditions for the tangent bundle of the Sasakian manifold to be quasi-conharmonically flat, φC-conharmonically flat and ξC-conharmonically flat concerning the quarter symmetric metric connection.