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 On some classes of weakly $Z$-symmetric manifolds Commun. Korean Math. Soc. 2020 Vol. 35, No. 3, 935-951 https://doi.org/10.4134/CKMS.c190275Published online March 16, 2020Printed July 31, 2020 Kingbawl Lalnunsiami, Jay Prakash Singh Mizoram University; Mizoram University Abstract : The aim of the paper is to study some geometric properties of weakly $Z$-symmetric manifolds. Weakly $Z$-symmetric manifolds with Codazzi type and cyclic parallel $Z$ tensor are studied. We consider Einstein weakly $Z$-symmetric manifolds and conformally flat weakly $Z$-symmetric manifolds. Next, it is shown that a totally umbilical hypersurface of a conformally flat weakly $Z$-symmetric manifolds is of quasi constant curvature. Also, decomposable weakly $Z$-symmetric manifolds are studied and some examples are constructed to support the existence of such manifolds. Keywords : Weakly $Z$-symmetric manifolds, Einstein weakly $Z$-symmetric manifolds, conformally flat weakly $Z$-symmetric manifolds, decomposable weakly $Z$-sym\-metric manifolds MSC numbers : Primary 53B20, 53B21, 53C25 Downloads: Full-text PDF   Full-text HTML