Ricci solitons in Lorentzian α-Sasakian manifolds

Bagewadi, C. S. and Ingalahalli, Gurupadavva (2012) Ricci solitons in Lorentzian α-Sasakian manifolds. ACTA MATHEMATICA ACADEMIAE PAEDAGOGICAE NYÍREGYHÁZIENSIS, 28 (1). pp. 59-68. ISSN 0866-0174

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Abstract

We study Ricci solitons in Lorentzian α-Sasakian manifolds. It is shown that a symmetric parallel second order covariant tensor in a Lorentzian α-Sasakian manifold is a constant multiple of the metric tensor. Using this it is shown that if LV g + 2S is parallel, V is a given vector field then (g, V ) is Ricci soliton. Further, by virtue of this result Ricci solitons for (2n + 1)-dimensional Lorentzian α-Sasakian manifolds are obtained. Next, Ricci solitons for 3-dimensional Lorentzian α-Sasakian manifold whose scalar curvature is constant are obtained.

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