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

Abstract

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