Second order parallel tensors on para r-Sasakian manifolds with a coefficient $\alpha$

Abstract: Levy [11] had proved that a second order symmetric parallel non singular tensor on a space of constant curvature is a constant multiple of the metric tensor. Sharma [6] has proved that second order parallel tensor in a Kaehler Space of constant holomorphic sectional curvature is a linear combination with constant coefficients of the Kaehlerian metric and the fundamental 2-form. In this paper, we show that a second order symmetric parallel tensor on a para $r$-Sasakian manifold with a coefficient $\alpha $ 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 para $r$-Sasakian manifold.

Keywords: Sasakian manifold, second order parallel tensors

Classification (MSC2000): 53C15; 53C25

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