On some classes of weakly $Z$-symmetric manifolds
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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.
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.
참고문헌 (25)
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