• Title, Summary, Keyword: special conformally flat

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ON SPECIAL CONFORMALLY FLAT SPACES WITH WARPED PRODUCT METRICS

  • Kim, Byung-Hak;Lee, Sang-Deok;Choi, Jin-Hyuk;Lee, Young-Ok
    • Journal of applied mathematics & informatics
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    • v.29 no.1_2
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    • pp.497-504
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    • 2011
  • In 1973, B. Y. Chen and K. Yano introduced the special conformally flat space for the generalization of a subprojective space. The typical example is a canal hypersurface of a Euclidean space. In this paper, we study the conditions for the base space B to be special conformally flat in the conharmonically flat warped product space $B^n{\times}_fR^1$. Moreover, we study the special conformally flat warped product space $B^n{\times}_fF^p$ and characterize the geometric structure of $B^n{\times}_fF^p$.

REMARKS ON CONFORMAL TRANSFORMATION ON RIEMANNIAN MANIFOLDS

  • Kim, Byung-Hak;Choi, Jin-Hyuk;Lee, Young-Ok
    • Journal of applied mathematics & informatics
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    • v.27 no.3_4
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    • pp.857-864
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    • 2009
  • The special conformally flatness is a generalization of a sub-projective space. B. Y. Chen and K. Yano ([4]) showed that every canal hypersurface of a Euclidean space is a special conformally flat space. In this paper, we study the conditions for the base space B is special conformally flat in the conharmonically flat warped product space $B^n{\times}f\;R^1$.

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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.