• Title, Summary, Keyword: indefinite Kenmotsu manifold

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TWO CHARACTERIZATION THEOREMS FOR HALF LIGHTLIKE SUBMANIFOLDS OF AN INDEFINITE KENMOTSU MANIFOLD

  • Jin, Dae Ho
    • The Pure and Applied Mathematics
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    • v.21 no.1
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    • pp.1-10
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    • 2014
  • In this paper, we study the curvature of locally symmetric or semi-symmetric half lightlike submanifolds M of an indefinite Kenmotsu manifold $\bar{M}$, whose structure vector field is tangent to M. After that, we study the existence of the totally geodesic screen distribution of half lightlike submanifolds of indefinite Kenmotsu manifolds with parallel co-screen distribution subject to the conditions: (1) M is locally symmetric, or (2) the lightlike transversal connection is flat.

LOCALLY SYMMETRIC HALF LIGHTLIKE SUBMANIFOLDS IN AN INDEFINITE KENMOTSU MANIFOLD

  • Jin, Dae-Ho
    • Communications of the Korean Mathematical Society
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    • v.27 no.3
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    • pp.583-589
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    • 2012
  • In this paper, we study locally symmetric half lightlike submanifolds M of an indefinite Kenmotsu manifold $\bar{M}$ subject to the conditions: (1) The transversal vector bundle $tr(TM)$ is parallel with respect to the connection $\bar{\nabla}$ of $\bar{M}$ and (2) M is irrotational.

NON-EXISTENCE OF TOTALLY GEODESIC SCREEN DISTRIBUTIONS ON LIGHTLIKE HYPERSURFACES OF INDEFINITE KENMOTSU MANIFOLDS

  • Jin, Dae Ho
    • Communications of the Korean Mathematical Society
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    • v.28 no.2
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    • pp.353-360
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    • 2013
  • We study lightlike hypersurfaces of indefinite Kenmotsu manifolds. The purpose of this paper is to prove that there do not exist totally geodesic screen distributions on semi-symmetric lightlike hypersurfaces of indefinite Kenmotsu manifolds with flat transversal connection.

Screen Slant Lightlike Submanifolds of Indefinite Kenmotsu Manifolds

  • Gupta, Ram Shankar;Upadhyay, Abhitosh
    • Kyungpook Mathematical Journal
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    • v.50 no.2
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    • pp.267-279
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    • 2010
  • In this paper, we introduce the notion of a screen slant lightlike submanifold of an indefinite Kenmotsu manifold. We provide characterization theorem for existence of screen slant lightlike submanifold with examples. Also, we give an example of a minimal screen slant lightlike submanifold of $R_2^9$ and prove some characterization theorems.

EQUIVALENCE CONDITIONS OF SYMMETRY PROPERTIES IN LIGHTLIKE HYPERSURFACES OF INDEFINITE KENMOTSU MANIFOLDS

  • Lungiambudila, Oscar;Massamba, Fortune;Tossa, Joel
    • Bulletin of the Korean Mathematical Society
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    • v.53 no.4
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    • pp.1259-1280
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    • 2016
  • The paper deals with lightlike hypersurfaces which are locally symmetric, semi-symmetric and Ricci semi-symmetric in indefinite Kenmotsu manifold having constant $\bar{\phi}$-holomorphic sectional curvature c. We obtain that these hypersurfaces are totally goedesic under certain conditions. The non-existence condition of locally symmetric lightlike hyper-surfaces are given. Some Theorems of specific lightlike hypersurfaces are established. We prove, under a certain condition, that in lightlike hyper-surfaces of an indefinite Kenmotsu space form, tangent to the structure vector field, the parallel, semi-parallel, local symmetry, semi-symmetry and Ricci semi-symmetry notions are equivalent.