Bonnet-Myers Theorem

From ProofWiki
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



Source of Name

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


Sources