Ricci Solitons in (ε,δ)-Trans-Sasakian Manifolds

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C.S. Bagewadi, Gurupadavva Ingalahalli, Ricci Solitons in (ε,δ)-Trans-Sasakian Manifolds, Int. J. Anal. Appl., 14 (2) (2017), 209-217.

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C.S. Bagewadi, Gurupadavva Ingalahalli

Abstract

We study Ricci solitons in (ε,δ)-trans-Sasakian manifolds. It is shown that a symmetric parallel second order covariant tensor in a (ε,δ)-trans-Sasakian manifold is a constant multiple of the metric tensor. Using this it is shown that if Vg + 2S is parallel where V is a given vector field, then (g,V) is Ricci soliton. Further, by virtue of this result, Ricci solitons for 3-dimensional (ε,δ)-trans-Sasakian manifolds are obtained. Also an example of Ricci solitons in 3-dimensional (ε,δ)-trans-Sasakian manifold is provided in the region where trans-Sasakian manifold is expanding (shrinking) the Lorentzian trans-Sasakian manifold is shrinking (expanding).

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