A geometrical interpretation of the null sectional curvature

A geometrical interpretation is given for the null sectional curvature of degenerate planes in a Lorentzian manifold. This interpretation is based on a generalization to the indefinite case of the squaroids of Levi-Civita. Further, it is shown that a three-dimensional, conformally flat Lorentzian manifold has isotropic and spatially constant null sectional curvature if and only if it is locally a Robertson–Walker manifold.