On extended generalized ϕ-recurrent Sasakian manifolds

The object of this paper is to introduce the notion of extended generalized ϕ-recurrency to Sasakian manifolds and study its various geometric properties with the existence by an interesting example. Among the results established here it is shown that an extended generalized ϕ-recurrent Sasakian manifold is an Einstein manifold. Further, we study extended generalized T–ϕ-recurrent Sasakian manifold and obtain the results which reveal the nature of its associated 1-forms. Finally, an example of a 3-dimensional extended generalized ϕ-recurrent Sasakian manifold which is neither ϕ-recurrent nor generalized ϕ-recurrent is constructed for illustration.