On Generalized Ricci-recurrent LP-sasakian Manifolds

Abstract

The object of the present paper is to study a generalized Ricci-recurrent LP-Sasakian manifold. Here we show that the generalized Ricci-recurrent LP-Sasakian manifold admitting cyclic Ricci tensor is an Einstein manifold.

On nearly Ricci recurrent manifolds

“…If the associated 1-form B becomes zero, then the manifold GK n reduces to recurrent manifold introduced by Ruse [8] and Waker [9] which was denoted by K n . In recent papers Arslan etal [10], Shaikh and Patra [11], Mallick,De and De [12], Khairnar [Kh], Shaikh, Prakasha and Ahmad [14], Kumar, Singh and Chowdhary [15], Hui [16], Singh and Mayanglambam [17], Singh and Kishor [18] etc. explored various geometrical propertis by using generlaized recurrent and generlaized Ricci recurrent manifold on Riemannian manifolds , Lorentzian Trans-Sasakian manifolds, LP-Sasakian manifolds, (k − µ) contact metric manifolds.…”