We study the Lie algebra of infinitesimal isometries on compact Sasakian and K–contact manifolds. On a Sasakian manifold which is not a space form or 3– Sasakian, every Killing vector field is an infinitesimal automorphism of the Sasakian structure. For a manifold with K–contact structure, we prove that there exists a Killing vector field of constant length which is not an infinitesimal automor...

We investigate some topological properties, in particular formality, of compact Sasakian manifolds. Answering some questions raised by Boyer and Galicki, we prove that all higher (than three) Massey products on any compact Sasakian manifold vanish. Hence, higher Massey products do obstruct Sasakian structures. Using this we produce a method of constructing simply connected K-contact non-Sasakia...

In this paper, we study indefinite trans-Sasakian manifold M̄ of quasi-constant curvature with lightlike hypersurfaces M . We provide several new results on such a manifold M̄ , in which the characteristic 1form θ and the characteristic vector field ζ, defined by (1.1), are identical with the structure 1-form θ and the structure vector field ζ of the indefinite trans-Sasakian structure (J, ζ, θ) ...

The Newman-Penrose-Perjes formalism is applied to Sasakian 3-manifolds and the local form of the metric and contact structure is presented. The local moduli space can be parameterised by a single function of two variables and it is shown that, given any smooth function of two variables, there exists locally a Sasakian structure with scalar curvature equal to this function. The case where the sc...

In ([1]), T. Adati and K. Matsumoto defined para-Sasakian and special para-Sasakian manifolds which are considered as special cases of an almost paracontact manifold introduced by I. Sato and K. Matsumoto ([10]). In the same paper, the authors studied conformally symmetric para-Sasakian manifolds and they proved that an ndimensional (n>3) conformally symmetric para-Sasakian manifold is conforma...

Warped product CR-submanifolds in Kählerian manifolds were intensively studied only since 2001 after the impulse given by B.Y. Chen in [2], [3]. Immediately after, another line of research, similar to that concerning Sasakian geometry as the odd dimensional version of Kählerian geometry, was developed, namely warped product contact CR-submanifolds in Sasakian manifolds (cf. [6], [7]). In this n...

The object of the present paper is to study generalized -recurrent Sasakian manifolds. Here it is proved that a generalized -recurrent Sasakian manifold is an Einstein manifold. We also find a relation between the associated 1-forms A and B for a generalized -recurrent and generalized concircular -recurrent Sasakian manifolds. Finally, we proved that a three dimensional locally generalized -rec...

In this paper we introduce the concept of (ε)-almost paracontact manifolds, and in particular, of (ε)-para Sasakian manifolds. Several examples are presented. Some typical identities for curvature tensor and Ricci tensor of (ε)-para Sasakian manifolds are obtained. We prove that if a semi-Riemannian manifold is one of flat, proper recurrent or proper Ricci-recurrent, then it can not admit an (ε...