Null submanifolds and statistical connections in indefinite Kähler manifolds

A holomorphic statistical connection in an indefinite K"ahler manifold induces in a natural way a statistical connection in a nondegenerate submanifold, but not if the submanifold is degenerate, due to the degeneracy of the induced metric.In the case of a null hypersurface in an indefinite K"ahler manifold, we construct a new nondegenerate metric on the null hypersurface and we study conditions for the induced connection to be statistical with respect to it. We also study the case of codimension two invariant null submanifolds.