Differential geometry Surfaces in Euclidean space Concept
Principal curvature
Summary
The principal curvatures of a surface at a point are the largest and the smallest bending of the surface over all tangent directions. They are the eigenvalues of the shape operator, and the corresponding eigenvectors are the principal directions. Their product is the Gaussian curvature and their average is the mean curvature.
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About this page
| Tag | FA8QE1SGP4 |
|---|---|
| URI | m2://FA8QE1SGP4 |
| Kind | concept |
| Writing | W0 stub |
| MSC | 53A05 |
| Same as | |
| Changed | 2 November 2026 |
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Used by
- Huisken's theorem on convex hypersurfaces
- Gaussian curvature
- Umbilical point
- Euler's theorem on normal curvatures
- Mean curvature