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

Résumé

The present paper aims to study the complete lifts of the quartersymmetric
metric connection and we establish the interrelation between Levi-Civita connection and quartersymmetric 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 quartersymmetric 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 quartersymmetric metric connection.