Almost $C(\lambda)$-manifolds

In this paper, we study almost $C(\lambda)$-manifolds. We obtain necessary and sufficient conditions for an almost contact metric manifold to be an almost $C(\lambda)$-manifold. We prove that contact analogs of A. Gray's second and third curvature identities on almost $C(\lambda)$-manifolds hold, while a contact analog of A. Gray's first identity holds if and only if the manifold is cosymplectic. It is proved that a conformally flat, almost $C(\lambda)$-manifold is a manifold of constant curvature $\lambda$.