On conformal and quasi-conformal curvature tensors of an $N(k)$-quasi Einstein manifold
Commun. Korean Math. Soc. 2012 Vol. 27, No. 2, 317-326
https://doi.org/10.4134/CKMS.2012.27.2.317
Published online June 1, 2012
Aliakbar Hosseinzadeh and Abolfazl Taleshian
Mazandaran University, Mazandaran University
Abstract : We consider $N(k)$-quasi Einstein manifolds satisfying the conditions $C(\xi,X).S=0$, $\tilde{C}(\xi,X).S=0$, $\bar{P}(\xi,X).C=0$, $P(\xi,X).\tilde{C}=0$ and $\bar{P}(\xi,X).\tilde{C}=0$ where $C$, $\tilde{C}$, $P$ and $\bar{P}$ denote the conformal curvature tensor, the quasi-conformal curvature tensor, the projective curvature tensor and the pseudo projective curvature tensor, respectively.
Keywords : $k$-nullity distribution, quasi Einstein manifold, $N(k)$-quasi Einstein manifold, conformal curvature tensor, quasi-conformal curvature tensor, projective curvature tensor, pseudo projective curvature tensor
MSC numbers : 53C25
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