The axiom of spheres in semi-Riemannian geometry with lightlike submanifolds

Abstract

Let $(\overline{M},\overline{g})$ be a semi-Riemannain manifold and (M, g, S (TM), S (TM⊥)) be its lightlike submanifold. We show that if $\overline{M}$ satisfies the axiom of r-planes & spheres then it is a real space form.