Second Order Parallel Tensors on α - Sasakian Manifold Lovejoy Das

Das, Lovejoy (2007) Second Order Parallel Tensors on α - Sasakian Manifold Lovejoy Das. ACTA MATHEMATICA ACADEMIAE PAEDAGOGICAE NYÍREGYHÁZIENSIS, 23 (1). pp. 65-69. ISSN 0866-0174

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Abstract

Levy 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 has proved that a second order parallel tensor in a Kaehler space of constant holomorphic sectional curvature is a linear combination with constant coefficients of the Kaehlarian metric andthe fundamental 2 – form. In this paper we show that a second order symmetric parallel tensor on an α – K contact (α ∈ Ro) manifold is a constant multiple of the associated metric tensor and we also prove that there is no nonzero skew symmetric second order parallel tensor on an α – Sasakian manifold.

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