Spacelike metric foliations

In this paper, we investigate spacelike metric foliations in lightlike complete spacetimes. When such a foliation satisfies the strong energy condition Ric(v)(e) greater than or equal to 0 for timelike vectors e, it must be totally geodesic, and the metric is of higher rank, in the sense that each point of the spacetime is contained inside a flat, totally geodesic, timelike rectangle. If in addition Ric(v)(a) = 0, then the metric is (at least locally) a product metric, with the leaves of the foliation tangent to one of the factors. (C) 1999 Elsevier Science B.V. All right reserved. Subj. Class.: Differential geometry; General relativity 1991 MSG: 53C12; 53C80; 83C75.