Osserman Lightlike Hypersurfaces on a Foliated Class of Lorentzian Manifolds

Abstract

This paper deals with a family of Osserman lightlike hypersurfaces (M u ) of a class of Lorentzian manifolds M̄ such that its each null normal vector is defined on some open subset of M̄ 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 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.