Ricci solitons in \(\alpha\)-Sasakian manifolds
Summary: We study Ricci solitons in \(\alpha\)-Sasakian manifolds. It is shown that a symmetric parallel second order-covariant tensor in a \(\alpha\)-Sasakian manifold is a constant multiple of the metric tensor. Using this, it is shown that if \(\mathcal L_V g + 2S\) is parallel where \(V\) is a given vector field, then \((g, V, \lambda)\) is a Ricci soliton. Further, by virtue of this result, Ricci solitons for \(n\)-dimensional \(\alpha\)-Sasakian manifolds are obtained. Next, Ricci solitons for 3-dimensional \(\alpha\)-Sasakian manifolds are discussed with an example.
scientific article; zbMATH DE number 6078638