Notes on weakly cyclic $Z$-symmetric manifolds
Bull. Korean Math. Soc. 2018 Vol. 55, No. 1, 227-237
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
Downloads: Full-text PDF  

Copyright © Korean Mathematical Society. All Rights Reserved.
The Korea Science Technology Center (Rm. 411), 22, Teheran-ro 7-gil, Gangnam-gu, Seoul 06130, Korea
Tel: 82-2-565-0361  | Fax: 82-2-565-0364  | E-mail:   | Powered by INFOrang Co., Ltd