$*$-Ricci tensor on three dimensional almost coK\"{a}hler manifolds

Abstract

In this paper, we obtain some classification results of three-dimensional non-coK\"{a}hler almost coK\"{a}hler manifold $M$ whose Reeb vector field is strongly normal unit vector field with $\xi(\|\nabla_\xi h\|)=0$, for which the $*$-Ricci tensor is of Codazzi-type or $M$ satisfies the curvature condition $Q^*\cdot R=0$.