Ricci Solitons in α-Sasakian Manifolds. (14th July 2012) - Ingalahalli, Gurupadavva; Bagewadi, C. S.
Abstract : We study Ricci solitons inα -Sasakian manifolds. It is shown that a symmetric parallel second order-covariant tensor in aα -Sasakian manifold is a constant multiple of the metric tensor. Using this, it is shown that ifℒ V g + 2 S is parallel whereV is a given vector field, then( g, V, λ ) is Ricci soliton. Further, by virtue of this result, Ricci solitons forn -dimensionalα -Sasakian manifolds are obtained. Next, Ricci solitons for 3-dimensionalα -Sasakian manifolds are discussed with an example.