Editing Hopf–Rinow theorem (section)

{{Short description|Gives equivalent statements about the geodesic completeness of Riemannian manifolds}}
The '''Hopf–Rinow theorem''' is a set of statements about the [[Geodesic manifold|geodesic completeness]] of [[Riemannian manifold]]s. It is named after [[Heinz Hopf]] and his student [[Willi Rinow]], who published it in 1931.<ref>{{cite journal|last1=Hopf|first1=H.|last2=Rinow|first2=W.|title=Ueber den Begriff der vollständigen differentialgeometrischen Fläche|journal=[[Commentarii Mathematici Helvetici]]|volume=3|year=1931|issue=1|pages=209–225|doi=10.1007/BF01601813}}</ref> [[Stefan Cohn-Vossen]] extended part of the Hopf–Rinow theorem to the context of certain types of [[metric space]]s.