Osserman Lightlike Hypersurfaces on a Foliated Class of Lorentzian Manifolds

摘要

This paper deals with a family of Osserman lightlike hypersurfaces $(M_u)$ of a? class of Lorentzian manifolds $ar{M}$ such that its each null normal vector is defined on some open subset of $ar{M}$ around $M_u$.? We prove that a totally umbilical family of lightlike hypersurfaces of a connected Lorentzian pointwise Osserman manifold of constant curvature is locally Einstein and pointwise ${cal F}-$Osserman, where our foliation approach provides the required algebraic symmetries of the induced curvature tensor. Also we prove two new characterization theorems for the family? of Osserman lightlike hypersurfaces, supported by a physical example of Osserman lightlike hypersurfaces of the Schwarzschild spacetime.