  In this paper, we study Jacobi operators associated to algebraic curvature
maps (tensors) on lightlike submanifolds M. We investigate conditions for an
induced Rie- mann curvature tensor to be an algebraic curvature tensor on M. We
introduce the notion of lightlike Osserman submanifolds and an example of
2-degenerate Osserman metric is given. Finally we give some results of symmetry
properties on lightlike hy- persurfaces from Osserman condition.
