Ricci Solitons in (ϵ)-Trans-Sasakian Manifolds

Abstract

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.