# Bonnet-Myers Theorem

Jump to navigation
Jump to search

## 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

This theorem requires a proof.You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by crafting such a proof.To discuss this page in more detail, feel free to use the talk page.When this work has been completed, you may remove this instance of `{{ProofWanted}}` from the code.If you would welcome a second opinion as to whether your work is correct, add a call to `{{Proofread}}` the page. |

## 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