Ricci n_parallel trans-Sasakian 3-manifolds

In this paper, we present a new characterization for a trans-Sasakian 3-manifold to be proper. More precisely, we prove that if a compact trans-Sasakian 3-manifold has -parallel Ricci operator, then the manifold is homothetic to a cosymplectic or a Sasakian 3-manifold or is of type (0; β ) with ∇ β = ξ ( β ) ξ. Key words: Trans-Sasakian 3-manifold, Ƞ-parallel Ricci operator