Lightlike foliations of semi-Riemannian manifolds1

Using screen distributions and lightlike transversal vector bundles we develop a theory of degenerate foliations of semiRiemannian manifolds. We build lightlike foliations of a semiRiemannian manifold by suspension of a group homomorphism φ : π1(B, x0) → Isom(T ). We compute the basic cohomology groups of the flow determined by a lightlike Killing vector field on a complete semi-Riemannian manifold. We prove a lightlike analog to Rummler’s formula and the transversal divergence theorem of F. Kamber et al., [4].