Hopf–Rinow theorem
theorem that, for a Riemannian manifold, geodesic completeness is equivalent to completeness as a metric space
Facts
5 properties- Instance of
- theorem
- Part of
- list of theorems[4]
- Maintained by WikiProject
- WikiProject Mathematics[7]
- Named after
- Heinz Hopf, Willi Rinow[2][3]
- Proved by
- Heinz Hopf, Willi Rinow[5][6]
🏷️ Also known as
en Hopf-Rinow theorem
en Hopf–Rinow theorem
de Satz von Hopf-Rinow
fi Hopfin–Rinowin lause
fr théorème de Hopf-Rinow
it Teorema di Hopf-Rinow
ja Hopf-Rinowの定理
ja ホップ・リノーの定理
ja 完備リーマン多様体
ko 호프-리노우 정리
nl Stelling van Hopf-Rinow
pt teorema de Hopf–Rinow
ru Теорема Хопфа — Ринова
ru Теорема Хопфа ― Ринова
ru Теорема Хопфа-Ринова
tr Hopf-Rinow teoremi
uk теорема Гопфа — Рінова
uk теорема Хопфа — Рінова
vi Định lý Hopf–Rinow
zh 霍普夫-里諾定理
🔖 Identifiers · 5
- Encyclopedia of Mathematics article ID
- Hopf-Rinow_theorem
- Freebase ID
- /m/032g7v
- MathWorld ID
- Hopf-RinowTheorem
- Microsoft Academic ID (discontinued)
- 2780813270
- ScienceDirect topic ID
- mathematics/hopf-rinow-theorem
🔗 Connections
Named after 2
Proved by 2
Created notable works 1
Instance of 1
Maintained by WikiProject 1
Part of 1
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Summary
Hopf–Rinow theorem is a theorem[1].