Zhu's theorem

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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 \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