Hopf and Rinow: completeness in differential geometry

What changed

Connected metric completeness with global geodesic existence and related properties for surfaces.

Scientific scope

The record is the exact two-author 1931 Commentarii Mathematici Helvetici paper, pp. 209–225. It does not absorb later generalizations, infinite-dimensional counterexamples or every modern equivalent formulation.

Evidence

The linked sources identify this contribution and its scope. WRS has not independently reconstructed the scientific claims. The record is the exact two-author 1931 Commentarii Mathematici Helvetici paper, pp. 209–225. It does not absorb later generalizations, infinite-dimensional counterexamples or every modern equivalent formulation.

Contributors

• Heinz Hopf · SCIENCE: Named source author of the scoped work; individual effort shares are not measured.
• Willi Rinow · SCIENCE: Named source author of the scoped work; individual effort shares are not measured.

• Digitized Commentarii Mathematici Helvetici volume 3
• DOI record for Hopf–Rinow paper

Provisional WRS assessment, edition 2026-10-16.1. Independent expert calibration is pending. This grade does not certify correctness or assign ownership.

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