Turkish Journal of Mathematics
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.
DOI
10.3906/mat-1206-1
Keywords
Lightlike hypersurface, semi-Riemannian manifold, admissible screen distribution, pseudo-Jacobi operator, Osserman condition, indefinite S-manifold
First Page
340
Last Page
352
Recommended Citation
BRUNETTI, L (2014). Osserman lightlike hypersurfaces of indefinite S-manifolds. Turkish Journal of Mathematics 38 (2): 340-352. https://doi.org/10.3906/mat-1206-1
