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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 wikiPageExternalLink p072450.htm.
- Gauss–Codazzi_equations wikiPageExternalLink Peterson-Mainardi-CodazziEquations.html.
- Gauss–Codazzi_equations wikiPageID "9633335".
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- Gauss–Codazzi_equations wikiPageRevisionID "654350412".
- Gauss–Codazzi_equations wikiPageWikiLink Basis_(linear_algebra).
- Gauss–Codazzi_equations wikiPageWikiLink Category:Curvature_(mathematics).
- Gauss–Codazzi_equations wikiPageWikiLink Category:Differential_geometry_of_surfaces.
- Gauss–Codazzi_equations wikiPageWikiLink Category:Riemannian_geometry.
- Gauss–Codazzi_equations wikiPageWikiLink Category:Surfaces.
- Gauss–Codazzi_equations wikiPageWikiLink Christoffel_symbols.
- Gauss–Codazzi_equations wikiPageWikiLink Cokernel.
- Gauss–Codazzi_equations wikiPageWikiLink Darboux_frame.
- Gauss–Codazzi_equations wikiPageWikiLink Delfino_Codazzi.
- Gauss–Codazzi_equations wikiPageWikiLink Differential_geometry.
- Gauss–Codazzi_equations wikiPageWikiLink Differential_geometry_of_surfaces.
- Gauss–Codazzi_equations wikiPageWikiLink Euclidean_space.
- Gauss–Codazzi_equations wikiPageWikiLink Exact_sequence.
- Gauss–Codazzi_equations wikiPageWikiLink Gaspare_Mainardi.
- Gauss–Codazzi_equations wikiPageWikiLink Gauss_map.
- Gauss–Codazzi_equations wikiPageWikiLink Gaussian_curvature.
- Gauss–Codazzi_equations wikiPageWikiLink Hypersurface.
- Gauss–Codazzi_equations wikiPageWikiLink Immersion_(mathematics).
- Gauss–Codazzi_equations wikiPageWikiLink Journal_de_lxc3x89cole_Polytechnique.
- Gauss–Codazzi_equations wikiPageWikiLink Laplace–Beltrami_operator.
- Gauss–Codazzi_equations wikiPageWikiLink Levi-Civita_connection.
- Gauss–Codazzi_equations wikiPageWikiLink Linear_independence.
- Gauss–Codazzi_equations wikiPageWikiLink Mean_curvature.
- Gauss–Codazzi_equations wikiPageWikiLink Metric_connection.
- Gauss–Codazzi_equations wikiPageWikiLink Minimal_surface.
- Gauss–Codazzi_equations wikiPageWikiLink Normal_bundle.
- Gauss–Codazzi_equations wikiPageWikiLink Parametric_surface.
- Gauss–Codazzi_equations wikiPageWikiLink Pierre_Ossian_Bonnet.
- Gauss–Codazzi_equations wikiPageWikiLink Pseudo-Riemannian_manifold.
- Gauss–Codazzi_equations wikiPageWikiLink Pushforward_(differential).
- Gauss–Codazzi_equations wikiPageWikiLink Riemann_curvature_tensor.
- Gauss–Codazzi_equations wikiPageWikiLink Riemannian_geometry.
- Gauss–Codazzi_equations wikiPageWikiLink Riemannian_manifold.
- Gauss–Codazzi_equations wikiPageWikiLink Rigid_transformation.
- Gauss–Codazzi_equations wikiPageWikiLink Second_fundamental_form.
- Gauss–Codazzi_equations wikiPageWikiLink Submanifold.
- Gauss–Codazzi_equations wikiPageWikiLink Symmetry_of_second_derivatives.
- Gauss–Codazzi_equations wikiPageWikiLink Tangent_bundle.
- Gauss–Codazzi_equations wikiPageWikiLink Theorema_Egregium.
- Gauss–Codazzi_equations wikiPageWikiLink Vector-valued_differential_form.
- Gauss–Codazzi_equations wikiPageWikiLinkText "Codazzi–Mainardi equations".
- Gauss–Codazzi_equations wikiPageWikiLinkText "Gauss–Codazzi equations".
- Gauss–Codazzi_equations wikiPageWikiLinkText "Gauss–Codazzi equation".
- Gauss–Codazzi_equations wikiPageWikiLinkText "Gauss–Codazzi equations".
- Gauss–Codazzi_equations wikiPageWikiLinkText "Gauss–Codazzi".
- Gauss–Codazzi_equations wikiPageWikiLinkText "Gauss–Codazzi–Mainardi".
- 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 wikiPageUsesTemplate Template:Citation.
- Gauss–Codazzi_equations wikiPageUsesTemplate Template:Curvature.
- Gauss–Codazzi_equations wikiPageUsesTemplate Template:Harvtxt.
- Gauss–Codazzi_equations wikiPageUsesTemplate Template:Reflist.
- Gauss–Codazzi_equations wikiPageUsesTemplate Template:Springer.
- 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 hypernym Equations.
- Gauss–Codazzi_equations type Redirect.
- Gauss–Codazzi_equations type Surface.
- 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 sameAs Q3589432.
- Gauss–Codazzi_equations sameAs Équations_de_Gauss-Codazzi.
- Gauss–Codazzi_equations sameAs m.02pmkqj.
- Gauss–Codazzi_equations sameAs Уравнения_Петерсона_―_Кодацци.
- Gauss–Codazzi_equations sameAs Q3589432.
- Gauss–Codazzi_equations wasDerivedFrom Gauss–Codazzi_equations?oldid=654350412.
- Gauss–Codazzi_equations isPrimaryTopicOf Gauss–Codazzi_equations.