Differential geometry Riemannian and pseudo-Riemannian manifolds Concept
Riemannian distance
Summary
The Riemannian distance between two points of a connected Riemannian manifold is the infimum of the lengths of the curves that join them. It turns the manifold into a metric space whose topology is the manifold topology. This distance is the bridge between the infinitesimal data of the Riemannian metric and global questions such as completeness, diameter and shortest paths.
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About this page
| Tag | B4QR306D8G |
|---|---|
| URI | m2://B4QR306D8G |
| Kind | concept |
| Writing | W0 stub |
| MSC | 53C20, 53B20 |
| Changed | 2 November 2026 |
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Used by
- Bishop–Gromov inequality
- Myers's theorem
- Toponogov's theorem
- Hopf–Rinow theorem
- Cheeger–Gromoll splitting theorem
- Space form
- Cut locus
- Myers–Steenrod theorem