Bonnet-Myers Theorem

Theorem

Let $M$ be a complete connected Riemannian manifold.

Suppose all the sectional curvatures of $M$ are bounded below by a positive constant.

Then $M$ is compact and has a finite fundamental group.

Proof

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Source of Name

This entry was named for Pierre Ossian Bonnet and Sumner Byron Myers.

Sources

• 2018: John M. Lee: Introduction to Riemannian Manifolds (2nd ed.) ... (previous) ... (next): $\S 1$: What Is Curvature? Curvature in Higher Dimensions