Differential geometry Surfaces in Euclidean space Concept
Gaussian curvature
Summary
The Gaussian curvature of a surface at a point is the product of its two principal curvatures. It is positive at dome-like points, negative at saddle-like points, and zero on surfaces that can be unrolled flat. By Gauss's Theorema Egregium it depends only on the first fundamental form, so it can be measured from inside the surface.
Where this leads
14 pages build on this one.
- Liouville's equation
- Index of the de Rham complex
- Gauss–Codazzi equations
- Willmore flow
- Gauss–Bonnet theorem
- Chern–Gauss–Bonnet theorem
- Minkowski problem
- Developable surface
- Hyperbolic geometry
- Decay of the Fourier transform of surface measure
- Hilbert's theorem on the hyperbolic plane
- Girard's theorem
- Theorema Egregium
- Stein–Tomas restriction theorem
Further reading
About this page
| Tag | SQVQ5DQT6W |
|---|---|
| URI | m2://SQVQ5DQT6W |
| Kind | concept |
| Writing | W0 stub |
| MSC | 53A05 |
| Same as |
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Used by
- Liouville's equation
- Gauss–Codazzi equations
- Willmore flow
- Gauss–Bonnet theorem
- Minkowski problem
- Developable surface
- Hyperbolic geometry
- Decay of the Fourier transform of surface measure
- Hilbert's theorem on the hyperbolic plane
- Theorema Egregium
- Stein–Tomas restriction theorem