Lightlike Osserman submanifolds of semi-Riemannian manifolds

Abstract

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.