Osserman lightlike hypersurfaces of indefinite S-manifolds

Authors : Letizia BRUNETTI

Pages : 340-352

Doi:10.3906/mat-1206-1

View : 12 | Download : 4

Publication Date : 0000-00-00

Article Type : Research Paper

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