Abstract

This paper deals with a family of Osserman lightlike hypersurfaces $(M_u)$ of a  class of Lorentzian manifolds $\bar{M}$ such that its each null normal vector is defined on some open subset of $\bar{M}$ 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.

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