TANGENT BUNDLES OF LP-SASAKIAN MANIFOLD ENDOWED WITH GENERALIZED SYMMETRIC METRIC CONNECTION

The aim of the present work is to study and establish conditions for an LP-Sasakian manifold on the tangent bundle TM. An LP-Sasakian manifold with the generalized symmetric metric connection on TM is investigated. Next, the curvature tensor and the Ricci tensor of an LP-Sasakian manifold with respect to the generalized symmetric metric connection on TM are calculated. Moreover, the projective curvature tensor with respect to the generalized symmetric metric connection on TM is studied and showed that TM is not (xi) over cap (C)-projectively flat. In particular, if alpha= 0 and beta = 1 then TM is (xi) over cap (C)-projectively flat.