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In this paper, we characterize almost co-Kähler manifolds with a conformal vector field. It is proven that if an almost co-Kähler manifold has a conformal vector field that is collinear with the Reeb vector field, then the manifold is a K-almost co-Kähler manifold. It is also shown that if a (κ, μ)-almost co-Kähler manifold admits a Killing vector field V, then either the manifold is K-almost co-Kähler or the vector field V is an infinitesimal strict contact transformation, provided that the (1,1) tensor h remains invariant under the Killing vector field. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to study Ricci semisymmetric paracontact metric manifolds satisfying ∇ ξ ⁡ h = 0 {\nabla_{\xi}h=0} and such that the sectional curvature of the plane section containing ξ equals a non-zero constant c. Also, we study paracontact metric manifolds satisfying the curvature condition Q ⋅ R = 0 {Q\cdot R=0} , where Q and R are the Ricci operator and the Riemannian curvature tensor, respectively, and second order symmetric parallel tensors in paracontact metric manifolds under the same conditions. Several consequences of these results are discussed. [ABSTRACT FROM AUTHOR]

The object of the present paper is to study generalized Sasakian-space-forms satisfying the curvature condition P(ξ, Y) - W = 0. Moreover, ø-M-projectively semisymmetric and ø-pseudo-projectively semisymmetric generalized Sasakian-space-forms are also studied. [ABSTRACT FROM AUTHOR]