Hopf–Rinow theorem

theorem that, for a Riemannian manifold, geodesic completeness is equivalent to completeness as a metric space
Intangible theorem Q2094241
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Hopf–Rinow theorem

Summary

Hopf–Rinow theorem is a theorem[1]. It draws 36 Wikipedia views per month (theorem category, ranking #241 of 1,306).[2]

Key Facts

  • Hopf–Rinow theorem's instance of is recorded as theorem[3].
  • Heinz Hopf is named after Hopf–Rinow theorem[4].
  • Willi Rinow is named after Hopf–Rinow theorem[5].
  • Hopf–Rinow theorem's part of is recorded as list of theorems[6].
  • Hopf–Rinow theorem's Freebase ID is recorded as /m/032g7v[7].
  • Hopf–Rinow theorem's proved by is recorded as Heinz Hopf[8].
  • Hopf–Rinow theorem's proved by is recorded as Willi Rinow[9].
  • Hopf–Rinow theorem's MathWorld ID is recorded as Hopf-RinowTheorem[10].
  • Hopf–Rinow theorem's maintained by WikiProject is recorded as WikiProject Mathematics[11].
  • Hopf–Rinow theorem's Microsoft Academic ID is recorded as 2780813270[12].
  • Hopf–Rinow theorem's Encyclopedia of Mathematics article ID is recorded as Hopf-Rinow_theorem[13].
  • Hopf–Rinow theorem's ScienceDirect topic ID is recorded as mathematics/hopf-rinow-theorem[14].

Why It Matters

Hopf–Rinow theorem draws 36 Wikipedia views per month (theorem category, ranking #241 of 1,306).[2] It has Wikipedia articles in 11 language editions, a strong signal of global cultural recognition.[15] It is known by 8 alternative names across languages and contexts.[16]

References

Programmatic citations — every numbered marker resolves to a verifiable graph row below.

Direct Wikidata claims

  1. [3] . wikidata.org.
  2. [4] . wikidata.org.
  3. [5] . wikidata.org.
  4. [6] . wikidata.org.
  5. [7] . Freebase Data Dumps. wikidata.org.
  6. [8] . wikidata.org.
  7. [9] . wikidata.org.
  8. [10] . wikidata.org.
  9. [11] . wikidata.org.
  10. [12] . wikidata.org.
  11. [13] . wikidata.org.
  12. [14] . wikidata.org.

Class ancestry

  1. [1] . Wikidata. wikidata.org.

Aggregate / graph-position facts

  1. [2] . Wikimedia Foundation. dumps.wikimedia.org.
  2. [15] . Wikidata sitelinks. wikidata.org.
  3. [16] . Wikidata aliases. wikidata.org.

📑 Cite this page

Use these citations when quoting this entity in research, articles, AI prompts, or wherever provenance matters. We aggregate Wikidata + Wikipedia + authoritative open-data sources; the stitched, scored, cross-referenced view is what 4ort.xyz contributes.

APA 4ort.xyz Knowledge Graph. (2026). Hopf–Rinow theorem. Retrieved May 3, 2026, from https://4ort.xyz/entity/hopf-rinow-theorem
MLA “Hopf–Rinow theorem.” 4ort.xyz Knowledge Graph, 4ort.xyz, 3 May. 2026, https://4ort.xyz/entity/hopf-rinow-theorem.
BibTeX @misc{4ortxyz_hopf-rinow-theorem_2026, author = {{4ort.xyz Knowledge Graph}}, title = {{Hopf–Rinow theorem}}, year = {2026}, url = {https://4ort.xyz/entity/hopf-rinow-theorem}, note = {Accessed: 2026-05-03}}
LLM prompt According to 4ort.xyz Knowledge Graph (aggregator of Wikidata, Wikipedia, and authoritative open-data sources): Hopf–Rinow theorem — https://4ort.xyz/entity/hopf-rinow-theorem (retrieved 2026-05-03)

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