Abstract.

The purpose of this paper is to study the notion of hyper generalized ϕ-recurrent (LCS)n-manifolds and its various geometric properties. Among the results established here, it is shown that a hyper generalized ϕ-recurrent (LCS)n-manifold is an Einstein manifold. Moreover, we prove that a locally hyper generalized ϕ-recurrent (LCS)n-manifold is of constant curvature. Finally, we consider a hyper generalized concircularly ϕ-recurrent (LCS)n-manifold and prove that it is an Einstein one.

Keywords:

(LCS)n-manifold, hyper generalized ϕ-recurrent manifold, Einstein manifold.