Killing and Geodesic Lightlike Hypersurfaces of Indefinite Sasakian Manifolds


Abstract: In this paper, we study a lightlike hypersurface of indefinite Sasakian manifold, tangent to the structure vector field \xi. Theorems on parallel and Killing distributions are obtained. Necessary and sufficient conditions have been given for lightlike hypersurface to be mixed totally geodesic, D-totally geodesic, D\perp<\xi>-totally geodesic and D'-totally geodesic. We prove that, if the screen distribution of lightlike hypersurface M of indefinite Sasakian manifold is totally umbilical, the D\perp<\xi>-geodesibility of M is equivalent to the D\perp<\xi>-parallelism of the distribution T M^\perp of rank 1 (Theorem \ref{Theoscre}). Finally, we give the D\perp<\xi>-version (Theorem 4.22) of the Theorem 2.2 ([11], page 88).

Keywords: Lightlike Hypersurfaces; Indefinite Sasakian; Screen Distribution

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