Bull. Korean Math. Soc. 2016; 53(4): 1259-1280
Printed July 31, 2016
https://doi.org/10.4134/BKMS.b150666
Copyright © The Korean Mathematical Society.
Oscar Lungiambudila, Fortun\'{e} Massamba, and Joel Tossa
Universit\'e de Kinshasa (UNIKIN), University of KwaZulu-Natal, Universit\'e d
The paper deals with lightlike hypersurfaces which are locally symmetric, semi-symmetric and Ricci semi-symmetric in indefinite Kenmotsu manifold having constant $\overline{\phi}$-holomorphic sectional curvature $c$. We obtain that these hypersurfaces are totally goedesic under certain conditions. The non-existence condition of locally symmetric lightlike hypersurfaces are given. Some Theorems of specific lightlike hypersurfaces are established. We prove, under a certain condition, that in lightlike hypersurfaces 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.
Keywords: indefinite Kenmotsu space form, locally symmetric lightlike hypersurface, semi-symmetric lightlike hypersurface, Ricci semi-symmetric lightlike hypersurface
MSC numbers: Primary 53C25; Secondary 53C40, 53C50
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