Manifolds with conullity at most two as graph manifolds
  We find necessary and sufficient conditions for a complete $n$-dimensional Riemannian manifold of finite volume, whose curvature tensor has nullity at least $n-2$, to be a geometric graph manifold. In the process, we show that Nomizu's conjecture, well known to be false in general, is true for manifolds with finite volume. 
Luis A. Florit and Wolfgang Ziller
math.DG math.GT