Axioms of spheres in lightlike geometry of submanifolds

We prove that if an indefinite Kaehler manifold \(\bar {M}\) with lightlike submanifolds satisfies the axioms of holomorphic 2r-spheres, axioms of holomorphic 2r-planes, axioms of transversal r-spheres and axioms of transversal r-planes, then it is an indefinite complex space form.