Resumen de Ricci solitons on para-Kähler manifold

Yadav Sunil Kumar

• The main purpose of the paper is to study the nature of Ricci soliton on para-K¨ahler manifolds satisfying some certain curvature conditions. In particular, if we consider certain pseudosymmetric and parallel symmetric tensor on para-K¨ahler 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-K¨ahler manifolds. Moreover, we obtain some results related to the quasi-conformal curvature tensor on such manifolds