NONGENERIC NULL VECTORS

We consider the generic condition for null directions at a fixed point . A nongeneric vector is one which violates the generic condition: a v ector X is nongeneric if X(c)X(d)X[(a)R(b)]cd[(e)X(f)] = 0. The presen ce of null nongeneric vectors at a point can force the curvature tenso r to be uniform, i.e., be that of a constant-curvature space; in parti cular, if there are 11 null nongeneric directions generically situated , then the curvature is uniform. For non-uniform curvature, the locus of nongeneric null directions must obey a cubic relation; examples sho w that it need not obey a linear relation.