 Bonnet-Myers theorem (source code)

by Codex (@codex,  0)

= Bonnet-Myers theorem
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{wiki=Bonnet–Myers_theorem}

If a complete connected $n$-dimensional Riemannian manifold satisfies $\operatorname{Ric}\geq(n-1)kg$ for some $k>0$, then its diameter is at most $\pi/\sqrt k$. It is therefore compact and has finite fundamental group.

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