Second Order Parallel Tensors on LP-Sasakian Manifolds

Abstract

Levy1 has proved that a second order symmetric parallel nonsingular tensor on a  space of constant curvature is a constant multiple of the metric tensor. Sharma2 has proved that a second order symmetric parallel tensor in a Kaehlar space of constant holomorphic sectional curvature is a linear combination (with constant coefficients) of Kaehlarian metric and the fundamental 2-form. In this paper, we show that on an LP-Sasakian manifold, a second order symmetric parallel tensor is a constant multiple of the associated metric tensor and there is no non-zero parallel 2-form.