• Title, Summary, Keyword: conformal Killing vector field

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THE CURVATURE OF HALF LIGHTLIKE SUBMANIFOLDS OF A SEMI-RIEMANNIAN MANIFOLD OF QUASI-CONSTANT CURVATURE

  • Jin, Dae Ho
    • The Pure and Applied Mathematics
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    • v.19 no.4
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    • pp.327-335
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    • 2012
  • We study half lightlike submanifolds M of semi-Riemannian manifolds $\widetilde{M}$ of quasi-constant curvatures. The main result is a characterization theorem for screen homothetic Einstein half lightlike submanifolds of a Lorentzian manifold of quasi-constant curvature subject to the conditions; (1) the curvature vector field of $\widetilde{M}$ is tangent to M, and (2) the co-screen distribution is a conformal Killing one.

LIGHTLIKE SUBMANIFOLDS OF A SEMI-RIEMANNIAN MANIFOLD WITH A SEMI-SYMMETRIC NON-METRIC CONNECTION

  • Jin, Dae-Ho
    • The Pure and Applied Mathematics
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    • v.19 no.3
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    • pp.211-228
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    • 2012
  • We study lightlike submanifolds M of a semi-Riemannian manifold $\bar{M}$ with a semi-symmetric non-metric connection subject to the conditions; (a) the characteristic vector field of $\bar{M}$ is tangent to M, (b) the screen distribution on M is totally umbilical in M and (c) the co-screen distribution on M is conformal Killing.

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.

TRANSVERSE HARMONIC FIELDS ON RIEMANNIAN MANIFOLDS

  • Pak, Jin-Suk;Yoo, Hwal-Lan
    • Bulletin of the Korean Mathematical Society
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    • v.29 no.1
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    • pp.73-80
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    • 1992
  • We discuss transverse harmonic fields on compact foliated Riemannian manifolds, and give a necessary and sufficient condition for a transverse field to be a transverse harmonic one and the non-existence of transverse harmonic fields. 1. On a foliated Riemannian manifold, geometric transverse fields, that is, transverse Killing, affine, projective, conformal fields were discussed by Kamber and Tondeur([3]), Molino ([5], [6]), Pak and Yorozu ([7]) and others. If the foliation is one by points, then transverse fields are usual fields on Riemannian manifolds. Thus it is natural to extend well known results concerning those fields on Riemannian manifolds to foliated cases. On the other hand, the following theorem is well known ([1], [10]): If the Ricci operator in a compact Riemannian manifold M is non-negative everywhere, then a harmonic vector field in M has a vanishing covariant derivative. If the Ricci operator in M is positive-definite, then a harmonic vector field other than zero does not exist in M.

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A CLASSIFICATION OF HALF LIGHTLIKE SUBMANIFOLDS OF A SEMI-RIEMANNIAN MANIFOLD WITH A SEMI-SYMMETRIC NON-METRIC CONNECTION

  • Jin, Dae Ho;Lee, Jae Won
    • Bulletin of the Korean Mathematical Society
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    • v.50 no.3
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    • pp.705-717
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    • 2013
  • In this paper, we study the geometry of half lightlike submanifolds M of a semi-Riemannian manifold $\tilde{M}$ with a semi-symmetric non-metric connection subject to the conditions; (1) the characteristic vector field of $\tilde{M}$ is tangent to M, the screen distribution on M is totally umbilical in M and the co-screen distribution on M is conformal Killing, or (2) the screen distribution is integrable and the local lightlike second fundamental form of M is parallel.