Second Order Parallel Tensors on LP-Sasakian Manifolds with a coefficient α

Das, Lovejoy S. (2017) Second Order Parallel Tensors on LP-Sasakian Manifolds with a coefficient α. ACTA MATHEMATICA ACADEMIAE PAEDAGOGICAE NYÍREGYHÁZIENSIS, 33 (1). pp. 85-89. ISSN 0866-0174

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Abstract

In 1926, Levy [3] had proved that a second order symmetric parallel nonsingular tensor on a space of constant curvature is a constant multiple of the metric tensor. Sharma [4] has proved that a second order parallel tensor in a K¨ahler space of constant holomorphic sectional curvature is a linear combination with constant coefficient of the K¨ahlerian 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 α (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.

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