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- Gauss–Codazzi_equations abstract "In Riemannian geometry, the Gauss–Codazzi–Mainardi equations are fundamental equations in the theory of embedded hypersurfaces in a Euclidean space, and more generally submanifolds of Riemannian manifolds. They also have applications for embedded hypersurfaces of pseudo-Riemannian manifolds.In the classical differential geometry of surfaces, the Gauss–Codazzi–Mainardi equations consist of a pair of related equations. The first equation, sometimes called the Gauss equation, relates the intrinsic curvature (or Gauss curvature) of the surface to the derivatives of the Gauss map, via the second fundamental form. This equation is the basis for Gauss's theorema egregium. The second equation, sometimes called the Codazzi–Mainardi equation, is a structural condition on the second derivatives of the Gauss map. It was named for Gaspare Mainardi (1856) and Delfino Codazzi (1868–1869), who independently derived the result, although it was discovered earlier by Peterson (1853).It incorporates the extrinsic curvature (or mean curvature) of the surface. The equations show that the components of the second fundamental form and its derivatives along the surface completely classify the surface up to a Euclidean transformation, a theorem of Ossian Bonnet.".
- Gauss–Codazzi_equations wikiPageID "9633335".
- Gauss–Codazzi_equations wikiPageRevisionID "598204889".
- Gauss–Codazzi_equations first "A.B.".
- Gauss–Codazzi_equations id "P/p072450".
- Gauss–Codazzi_equations last "Ivanov".
- Gauss–Codazzi_equations title "Peterson–Codazzi equations".
- Gauss–Codazzi_equations year "2001".
- Gauss–Codazzi_equations subject Category:Curvature_(mathematics).
- Gauss–Codazzi_equations subject Category:Differential_geometry_of_surfaces.
- Gauss–Codazzi_equations subject Category:Riemannian_geometry.
- Gauss–Codazzi_equations subject Category:Surfaces.
- Gauss–Codazzi_equations comment "In Riemannian geometry, the Gauss–Codazzi–Mainardi equations are fundamental equations in the theory of embedded hypersurfaces in a Euclidean space, and more generally submanifolds of Riemannian manifolds. They also have applications for embedded hypersurfaces of pseudo-Riemannian manifolds.In the classical differential geometry of surfaces, the Gauss–Codazzi–Mainardi equations consist of a pair of related equations.".
- Gauss–Codazzi_equations label "Gauss–Codazzi equations".
- Gauss–Codazzi_equations label "Équations de Gauss-Codazzi".
- Gauss–Codazzi_equations label "Уравнения Петерсона ― Кодацци".
- Gauss–Codazzi_equations sameAs Gauss%E2%80%93Codazzi_equations.
- Gauss–Codazzi_equations sameAs Équations_de_Gauss-Codazzi.
- Gauss–Codazzi_equations sameAs Q3589432.
- Gauss–Codazzi_equations sameAs Q3589432.
- Gauss–Codazzi_equations wasDerivedFrom Gauss–Codazzi_equations?oldid=598204889.