W_5 curvature tensor

SO Pambo, Moindi SK, Nzimbi BM. "A study of eta-Ricci soliton on W_5-semi symmetric LP sasakian manifolfds." International Journal of Statistics and Applied Mathematics. 2021;5(5):25-29. AbstractWebsite

In this paper, we study ƞ-Ricci solitons on Lorentzian para-Sasakian manifold satisfying
R(ξ,X)•W_5(Y,Z)U=0 and W_5(ξ,X)•R(Y,Z)U=0 conditions.
We prove that on a Lorentzian para-Sasakian manifold (M,ξ,ƞ,g), the Ricci curvature tensor satisfying
any one of the given conditions, the existence of ƞ-Ricci soliton then implies that (M,g) is Einstein
manifold. We also conclude that in these cases, there is no Ricci soliton on M, with the potential vector
field ξ (the killing vector)

SO Pambo, Moindi SK, Nzimbi BM. "A study of eta-Ricci soliton on W_5-semi symmetric LP sasakian manifolfds." International Journal of Statistics and Applied Mathematics. 2020;5(5):25-29. AbstractWebsite

In this paper, we study ƞ-Ricci solitons on Lorentzian para-Sasakian manifold satisfying
R(ξ,X)•W_5(Y,Z)U=0 and W_5(ξ,X)•R(Y,Z)U=0 conditions.
We prove that on a Lorentzian para-Sasakian manifold (M,ξ,ƞ,g), the Ricci curvature tensor satisfying
any one of the given conditions, the existence of ƞ-Ricci soliton then implies that (M,g) is Einstein
manifold. We also conclude that in these cases, there is no Ricci soliton on M, with the potential vector
field ξ (the killing vector).

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