Manifolds with conullity at most two as graph manifolds

Abstract

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.

22 pages, 8 figures. Two references added plus minor corrections

References in corpus (1)

• Three-manifolds with many flat planes

Cited by in corpus (3)

• Three-manifolds with many flat planes
• Non-negative Curvature and Conullity of the Curvature Tensor
• Geometric Graph Manifolds with non-negative scalar curvature