H-Ricci Solitons Onw3 Andw5 Semi-Symmetric Lp-Sasakian Manifolds

Abstract

The goal of this project is to study some properties of h-Ricci soliton on LP-Sasakian manifolds. In this work, h-Ricci solitons on LP-Sasakian manifolds which satisfy the semi-symmetric conditions R(X;Y) R(Z;U) = 0[28],also given by U.C. De [34] are considered. Particularly, we based our study on R(x ;X):W3(Y;Z) = 0 and R(x ;X):W5(Y;Z) = 0 The study is motivated by the results that are obtained in h-Ricci solitons on Para-kenmotsu manifolds. This led us to study or simply to investigate the h-Ricci solitons on W3 and W5 semi-symmetric LP-Sasakian manifolds satisfying the same conditions and see if a similar results are obtained.In addition, we prove that W3 and W5 semi-symmetric LPSasakian manifolds satisfying the semi-symmetric conditions R(x ;X):W3(Y;Z) = 0 and R(x ;X):W5(Y;Z) = 0; and having the h-Ricci soliton structure are Einstein according to the value of l and a further conditions W3(x ;X) R(Y;Z) = 0 andW5(x ;X) R(Y;Z) = 0 where dot denote the derivative of algebra at every point of a tangent space,say Tp(U).