Second Order Parallel Tensors on LP-Sasakian Manifolds with a coefficient $\alpha$

Abstract: In 1926, Levy had proved that a second order symmetric parallel nonsingular tensor on a space of constantvcurvature is a constant multiple of the metric tensor. Sharma has provedvthat a second order parallel tensor in a Kahler space of constant holomorphic sectional curvature is a linear combination with constant coefficient of the Kahlerian metric and the fundamental 2-form. In this paper, we have shown that a second order symmetric parallel tensor on Lorentzian Para Sasakian manifold (briefly LP-Sasakian) with a coefficient $\alpha$ (non zero scalar function) is a constant multiple of the associated metric tensor and we have also proved that there is no non zero skew symmetric second order parallel tensor on a LP-Sasakian manifold.

Keywords: Second Order parallel tensor, LP-Sasakian manifold with a coefficient, Parallel 2-form

Classification (MSC2000): 53C15; 53C25

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