Notes on weakly cyclic $Z$-symmetric manifolds
Bull. Korean Math. Soc. 2018 Vol. 55, No. 1, 227-237
https://doi.org/10.4134/BKMS.b160935
Published online January 31, 2018
Jaeman Kim
Kangwon National University
Abstract : In this paper, we study some geometric structures of a weakly cyclic $Z$-symmetric manifold (briefly, $[WCZS]_{n}$). More precisely, we prove that a conformally flat $[WCZS]_{n}$ satisfying certain conditions is special conformally flat and hence the manifold can be isometrically immersed in an Euclidean manifold $E^{n+1}$ as a hypersurface if the manifold is simply connected. Also we show that there exists a $[WCZS]_{4}$ with one parameter family of its associated 1-forms.
Keywords : weakly cyclic $Z$-symmetric manifolds, quasi Einstein, conformal Killing vector field, parallel vector field, special conformally flat, hypersurface
MSC numbers : 53A55, 53B20
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