Student Bio
Samwel O. Pambo, B.Ed (Science) -Mathematics major M.Sc (Applied Mathematics)-Study of Eta-Ricci Soliton. Areas of Interest: ODE(s), PDE(s), Geometry, Numerical Analysis, Dynamical Systems.
Project Summary
Project Title:Eta- Ricci Soliton on W_3 and W_5-Semi Symmetric LP Sasakian Manifolfds
Abstract
The goal of this project is to study some properties of eta-Ricci soliton on LP-Sasakian manifolds. In this work, eta-Ricci solitons on LP-Sasakian manifolds which satisfy the semi-symmetric conditions R(X,Y).R(Z,U)=0 also given by U.C. De are considered. Particularly, we based our study on R(\xi,X).W_3(Y,Z)=0 and R(\xi,X).W_5(Y,Z)=0 The study is motivated by the results that are obtained in eta-Ricci solitons on Para-kenmotsu manifolds. This led us to study or simply to investigate the eta-Ricci solitons on W_3 and W_5 semi-symmetric LP-Sasakian manifolds satisfying the same conditions and see if a similar results are obtained. In addition, we prove that W_3 and W_5 semi-symmetric LP-Sasakian manifolds satisfying the semi-symmetric conditions R(\xi,X).W_3(Y,Z)=0 and R(\xi,X).W_5(Y,Z)=0, and having the eta-Ricci soliton structure are Einstein according to the value of lambda and a further conditions W_3(\xi,X).R(Y,Z)=0$ and $W_5(\xi,X). R(Y,Z)=0 where dot denote the derivative of algebra at every point of a tangent space, say $T_{p}(U)$.