Assertion: ricci curvature | /r/HasAspect | topological implications
Facets:
value: excluding the case of surfaces
type: OTHER
Source sentences:
text: Briefly, positive Ricci curvature of a Riemannian manifold has strong topological consequences, while (for dimension at least 3), negative Ricci curvature has no topological implications.
text: By contrast, excluding the case of surfaces, negative Ricci curvature is now known to have no topological implications; Lohkamp (1994) has shown that any manifold of dimension greater than two admits a complete Riemannian metric of negative Ricci curvature.