SOME RESULTS ON LP-SASAKIAN MANIFOLDS WITH SEMI-SYMMETRIC METRIC CONNECTION

摘要

The object of the present paper is to study semi-symmetric metric connection on Lorentzian Para-Sasakian Manifolds. First section deals with the extensive history about introduction of LP-Sasakian manifolds. Preliminary ideas about the manifold is given in the next section which are indispensable for our derivations. In the succeeding section we present a brief survey of the necessary condition under which the Contact vector field on a Lorentzian para-Sasakian manifolds leaving the Ricci tensor with respect to semi-symmetric connection is a strict Contact vector field. In the following section we have extended our study for establishing a condition under which generalized ?-recurrent n = 2m + 1-dimensional LP-Sasakian manifold with respect to semi-symmetric metric connection will be an Einstein manifold. Further we have considered a Lorentzian para-Sasakian manifolds with respect to semi-symmetric metric connection admitting a Conharmonic Curvature tensor and a non-zero Ricci tensor satisfying L(X. Y)S = 0, and we have derived that the modulus of non-zero eigen values of the endomorphism Q of the tangent space corresponding to S is 2(n — 1). Lastly we have cited an example of LP-Sasakian manifold with semi-symmetric metric connection.