Infinitesimal null isotropy and Robertson–Walker metrics

The concept of infinitesimal null isotropy is defined for a Lorentz manifold, in terms of null sectional curvature (as defined by Harris). It is shown that infinitesimal null isotropy is equivalent to infinitesimal spatial isotropy (as defined by Karcher), and that a null-isotropic space for which null sectional curvature is infinitesimally spatially constant must have a Robertson–Walker metric.