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Ricci Solitons in (ϵ)-Trans-Sasakian Manifolds


Gurupadavva Ingalahalli and C. S. Bagewadi


We study Ricci solitons in (ϵ)-trans-Sasakian manifolds. It is shown that
a symmetric parallel second order covariant tensor in a (ϵ)-trans-Sasakian manifold is a constant multiple of the metric tensor. Using this it is shown that
if LV g + 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 n-dimensional (ϵ)-
trans-Sasakian Manifolds are obtained. Next, Ricci solitons for 3-dimensional
(ϵ)-trans-Sasakian Manifolds of type (α, β) are discussed.

Keywords and Phrases : Ricci soliton, (ϵ)-trans-Sasakian manifold, Einstein
AMS Subject Classification : : 53C15, 53C20, 53C21, 53C25, 53D10.

Received date : 4 May, 2011

Accepted date: January 09, 2012

cited by: J.T.S. Vol. 6 No.1 (2012), pp.145-159

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