Osserman lightlike hypersurfaces of indefinite $\mathcal S$-manifolds

Abstract

We mainly deal with the problem of admissibility for screen distributions on a lightlike hypersurface of both a semi-Riemannian manifold and an indefinite S -manifold. In the latter case, we first show that a characteristic screen distribution is never admissible, and then we provide a characterization for admissible screen distributions on proper totally umbilical lightlike hypersurfaces. Finally, in studying Osserman conditions, we characterize Osserman totally umbilical hypersurfaces of a semi-Riemannian manifold, obtaining explicit results on the eigenvalues of the pseudo-Jacobi operators in the case of lightlike hypersurfaces with Lorentzian screen leaves.

Osserman Lightlike Hypersurfaces on a Foliated Class of Lorentzian Manifolds

“…To the best of our knowledge, at the time of writing this paper, there are the (Atindogbe-Duggal's, 2009) paper and (Atindogbe et. el., 2011, Brunette, 2014 on the Osserman lightlike geometry, using an admissible screen distribution. Since lightlike (also called degenerate) geometry has been studied by several ways other than using a screen for specific problems (for example, see (Akivis-Goldberg 2000, Leistner, 2006 one may ask the following question.…”