Ricci solitons on para-Kähler manifolds

Abstract

The main purpose of the paper is to study the nature of Ricci soliton on para-Kähler manifolds satisfying some certain curvature conditions. In particular, if we consider certain pseudosymmetric and parallel symmetric tensor on para-Kähler manifolds we prove that V is solenoidal if and only if it is shrinking or steady or expanding depending upon the sign of scalar curvature for dimension M > 4, where (g; V; λ) be a Ricci soliton in a paraholomorphic projectively, pseudosymmetric para-Kähler manifolds. Moreover, we obtain some results related to the quasi-conformal curvature tensor on such manifolds.