• Title, Summary, Keyword: weakly cyclic Z-symmetric manifolds

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NOTES ON WEAKLY CYCLIC Z-SYMMETRIC MANIFOLDS

  • Kim, Jaeman
    • Bulletin of the Korean Mathematical Society
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    • v.55 no.1
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    • pp.227-237
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    • 2018
  • In this paper, we study some geometric structures of a weakly cyclic Z-symmetric manifold (briefly, $[W CZS]_n$). More precisely, we prove that a conformally flat $[W CZS]_n$ 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 $[W CZS]_4$ with one parameter family of its associated 1-forms.