Communications of the
Korean Mathematical Society
CKMS

ISSN(Print) 1225-1763 ISSN(Online) 2234-3024

Article

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Commun. Korean Math. Soc. 2012; 27(2): 317-326

Printed June 1, 2012

https://doi.org/10.4134/CKMS.2012.27.2.317

Copyright © The Korean Mathematical Society.

On conformal and quasi-conformal curvature tensors of an $N(k)$-quasi Einstein manifold

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