- Turkish Journal of Mathematics
- Vol: 38 Issue: 2
- Osserman lightlike hypersurfaces of indefinite S-manifolds
Osserman lightlike hypersurfaces of indefinite S-manifolds
Authors : Letizia Brunetti
Pages : 340-352
Doi:10.3906/mat-1206-1
View : 13 | Download : 7
Publication Date : 9999-12-31
Article Type : Makaleler
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.Keywords : Lightlike hypersurface, semi-Riemannian manifold, admissible screen distribution, pseudo-Jacobi operator, Osserman condition, indefinite S-manifold