Reduction of the codimension for degenerate submanifolds

Abstract

We give in this paper sufficient conditions for $r$-lightlike submanifolds $M$ of dimension $m$, which is not totally geodesic in an $(m+n)$-dimensional semi-Riemannian manifold of constant curvature $c$ to admit a reduction of codimension. We consider proper $r$-lightlike, coisotrope and totally lightlike submanifolds, generalizing thus previous results on isotropic submanifolds [1] as well as in the Riemannian case developed in [2, 5, 10].