Differential geometry Riemannian and pseudo-Riemannian manifolds Concept
Isometry of Riemannian manifolds
Summary
An isometry of Riemannian manifolds is a diffeomorphism that carries one Riemannian metric to the other. Two isometric manifolds are the same for Riemannian geometry: lengths, angles, geodesics and curvature correspond. The isometries of a manifold onto itself form a group, which by the Myers–Steenrod theorem is a Lie group.
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About this page
| Tag | R9YWQS15AA |
|---|---|
| URI | m2://R9YWQS15AA |
| Kind | concept |
| Writing | W0 stub |
| MSC | 53C20, 53B20 |
| Specializes | Isometry |
| Changed | 2 November 2026 |
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Definitions
Used by
- Symmetric space
- Killing–Hopf theorem
- Positive mass theorem
- Cheeger–Gromoll splitting theorem
- Myers–Steenrod theorem