A characterization of Robertson-Walker spaces by null sectional curvature

Abstract

ForN a null vector andA a vector perpendicular toN, define the null sectional curvature, with respect to TV, of the planeN ΛA ask N(N ΛA) = 〈R(N,A)A,N〉∼<A,A∼.Then Robertson-Walker metrics can be locally characterized as those for whichk n at each point is a constant for all the null plans at that point (in each null direction,N must be appropriately chosen). A global characterization of Robertson-Walker spaces is achieved by adding completeness and causality hypotheses.