Zhu's theorem

This article describes a result related to the Ricci curvature of a Riemannian manifold

Statement

Any complete open Riemannian manifold of nonnegative Ricci curvature is diffeomorphic to $\mathbb {R} ^{3}$.

Relation with other results

Schoen-Yau theorem

Further information: Schoen-Yau theorem

This drops the completeness assumption but strengthens the nonnegativity assumption on Ricci curvature to a positivity assumption.

References

• On open 3-manifolds of quasi-positive Ricci curvature by Shun-Hui Zhu