Ricci Solitons in α-Sasakian Manifolds

Abstract EN

We study Ricci solitons in α-Sasakian manifolds.

It is shown that a symmetric parallel second order-covariant tensor in a α-Sasakian manifold is a constant multiple of the metric tensor.

Using this, it is shown that if ℒVg+2S is parallel where V is a given vector field, then (g,V,λ) is Ricci soliton.

Further, by virtue of this result, Ricci solitons for n-dimensional α-Sasakian manifolds are obtained.

Next, Ricci solitons for 3-dimensional α-Sasakian manifolds are discussed with an example.