Bulletin of the
Korean Mathematical Society BKMS

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