Differential geometry Surfaces in Euclidean space Concept
Regular surface
Summary
A regular surface is a subset of that looks, near each of its points, like a smoothly bent piece of the plane. Near each point it is the image of a smooth injective map from an open set of the plane, with linearly independent partial derivatives. Regular surfaces are the setting of the classical differential geometry of surfaces: tangent planes, fundamental forms and curvatures are defined on them.
Where this leads
17 pages build on this one.
- Geodesic curvature
- Gauss–Codazzi equations
- Constant-mean-curvature surface
- Gaussian curvature
- Principal curvature
- Shape operator
- Second fundamental form
- Willmore energy
- First fundamental form
- Minimal surface
- Gauss–Bonnet theorem
- Chern–Gauss–Bonnet theorem
- Umbilical point
- Developable surface
- Euler's theorem on normal curvatures
- Mean curvature
- Theorema Egregium
Further reading
About this page
| Tag | 6080X3FAD4 |
|---|---|
| URI | m2://6080X3FAD4 |
| Kind | concept |
| Writing | W0 stub |
| MSC | 53A05 |
| Changed | 2 November 2026 |
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Used by
- Geodesic curvature
- Gauss–Codazzi equations
- Constant-mean-curvature surface
- Gaussian curvature
- Principal curvature
- Shape operator
- Second fundamental form
- Willmore energy
- First fundamental form
- Minimal surface
- Gauss–Bonnet theorem
- Umbilical point
- Developable surface
- Euler's theorem on normal curvatures
- Mean curvature
- Theorema Egregium