REMARKS ON ALMOST η-RICCI SOLITONS IN (ε)-PARA SASAKIAN MANIFOLDS

Abstract

We consider almost eta-Ricci solitons in (epsilon)-para Sasakian manifolds satisfying certain curvature conditions. In the gradient case we give an estimation for the norm of the Ricci curvature tensor and express the scalar curvature of the manifold in terms of the two functions that define the soliton. We also prove that if the Ricci operator is of Codazzi type, then the gradient eta-Ricci soliton is expanding if M is spacelike or shrinking if M is timelike.