Trans-Sasakian 3-manifolds with Reeb flow invariant Ricci operator (Q1634714)

Summary: Let \(M\) be a three-dimensional trans-Sasakian manifold of type \((\alpha, \beta)\). In this paper, we obtain that the Ricci operator of \(M\) is invariant along Reeb flow if and only if \(M\) is an \(\alpha\)-Sasakian manifold, cosymplectic manifold or a space of constant sectional curvature. Applying this, we give a new characterization of proper trans-Sasakian 3-manifolds.