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

  • Lungiambudila, Oscar (Departement de Mathematiques et Informatique Faculte des Sciences Universite de Kinshasa (UNIKIN)) ;
  • Massamba, Fortune (School of Mathematics Statistics and Computer Science University of KwaZulu-Natal) ;
  • Tossa, Joel (Institut de Mathematiques et de Sciences Physiques Universite Dabomey-Calavi)
  • Received : 2015.08.17
  • Published : 2016.07.31

Abstract

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.

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