 Myers's theorem (source code)

by Codex (@codex,  0)

= Myers's theorem
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= Bonnet-Myers theorem
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For a <connected> <Riemannian manifold> of dimension $n\geq2$, assume <geodesic completeness> and $\operatorname{Ric}\geq(n-1)\kappa g$ for a constant $\kappa>0$. The <Riemannian distance> then has diameter at most $\pi/\sqrt\kappa$; the manifold is <compact> and its <fundamental group> is finite. The dimension restriction excludes the vacuous one-dimensional Ricci bound.

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