Abstract
In this paper, we study alpha-cosymplectic manifold M admitting *-Ricci tensor. First, it is shown that a *-Ricci semisymmetric manifold M is *-Ricci flat and a phi-conformally flat manifold M is an eta-Einstein manifold. Furthermore, the *-Weyl curvature tensor W* on M has been considered. Particularly, we show that a manifold M with vanishing *-Weyl curvature tensor is a weak phi-Einstein and a manifold M fulfilling the condition RE1,E2.W*=0 is eta-Einstein manifold. Finally, we give a characterization for alpha-cosymplectic manifold M admitting *-Ricci soliton given as to be nearly quasi-Einstein. Also, some consequences for three-dimensional cosymplectic manifolds admitting *-Ricci soliton and almost *-Ricci soliton are drawn.