Cohn-Vossen theorem

This result is about manifolds in dimension:2

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

Statement

Any complete open nonnegatively curved Riemannian manifold of dimension 2 is either diffeomorphic to $\mathbb {R} ^{2}$ or flat.

Relation with other results

Related results

• Gromoll-Meyer theorem
• Schoen-Yau theorem
• Zhu's theorem

Related conjectures

• Cheeger-Gromoll conjecture
• Schoen-Yau conjecture