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.
Lightlike hypersurface, semi-Riemannian manifold, admissible screen distribution, pseudo-Jacobi operator, Osserman condition, indefinite S-manifold
"Osserman lightlike hypersurfaces of indefinite S-manifolds,"
Turkish Journal of Mathematics: Vol. 38:
2, Article 15.
Available at: https://journals.tubitak.gov.tr/math/vol38/iss2/15