• Title, Summary, Keyword: locally symmetric lightlike hypersurface

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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.