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NOTES ON WEAKLY CYCLIC Z-SYMMETRIC MANIFOLDS

  • Kim, Jaeman (Department of Mathematics Education Kangwon National University)
  • Received : 2016.11.21
  • Accepted : 2017.06.08
  • Published : 2018.01.31

Abstract

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.

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