Lorentzian Manifolds having the Killing Property

We deal with a Lorentzian n-dimensional manifold M carrying two skew-symmetric Killing null vector fields ξ1 and ξn. They define a commutative left invariant pairing. The (n – 2)-dimensional spatial distribution orthogonal to ξ1 and ξn is involutive and its leaves are totally geodesic and pseudo-isotropic. If n = 4, then it is shown that the general space-time M is of type D in Petrovʹs classification and the spatial surfaces which foliate M are totally geodesic and pseudo-isotropic. Properties of the congruence of Debever are pointed-out.