Lightlike Osserman submanifolds of semi-Riemannian manifolds

In this paper, we study Jacobi operators associated to algebraic curvature maps (tensors) on lightlike submanifolds M . We investigate conditions for an induced Riemann 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 hypersurfaces from Osserman condition.