Quasi-conformal curvature tensor on $N\left(k\right)$-quasi Einstein manifolds
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Abstract
This paper deals with the study of $N\left(k\right)$-quasi Einstein manifolds that satisfies the certain curvature conditions $\mathscr{C}_{\ast}\cdot\mathscr{C}_{\ast}=0,$ $\mathcal{S}\cdot\mathscr{C}_{\ast}=0$ and $\mathcal{R}\cdot\mathscr{C}_{\ast}=f\tilde{Q}\left(g,\mathscr{C}_{\ast}\right)$, where $\mathscr{C}_{\ast}$, $\mathcal{S}$ and $\mathcal{R}$ denotes the quasi-conformal curvature tensor, Ricci tensor and the curvature tensor respectively. Finally, we construct an example of $N\left(k\right)$-quasi Einstein manifold.
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References
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