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- Gauss_map abstract "In differential geometry, the Gauss map (named after Carl F. Gauss) maps a surface in Euclidean space R3 to the unit sphere S2. Namely, given a surface X lying in R3, the Gauss map is a continuous map N: X → S2 such that N(p) is a unit vector orthogonal to X at p, namely the normal vector to X at p.The Gauss map can be defined (globally) if and only if the surface is orientable, in which case its degree is half the Euler characteristic. The Gauss map can always be defined locally (i.e. on a small piece of the surface). The Jacobian determinant of the Gauss map is equal to Gaussian curvature, and the differential of the Gauss map is called the shape operator.Gauss first wrote a draft on the topic in 1825 and published in 1827.There is also a Gauss map for a link, which computes linking number.".
- Gauss_map thumbnail Gauss_map.svg?width=300.
- Gauss_map wikiPageExternalLink index.html.
- Gauss_map wikiPageID "378881".
- Gauss_map wikiPageLength "4776".
- Gauss_map wikiPageOutDegree "39".
- Gauss_map wikiPageRevisionID "676616243".
- Gauss_map wikiPageWikiLink Asymptotic_curve.
- Gauss_map wikiPageWikiLink Carl_Friedrich_Gauss.
- Gauss_map wikiPageWikiLink Catastrophe_theory.
- Gauss_map wikiPageWikiLink Category:Carl_Friedrich_Gauss.
- Gauss_map wikiPageWikiLink Category:Differential_geometry.
- Gauss_map wikiPageWikiLink Category:Differential_geometry_of_surfaces.
- Gauss_map wikiPageWikiLink Category:Riemannian_geometry.
- Gauss_map wikiPageWikiLink Category:Surfaces.
- Gauss_map wikiPageWikiLink Clint_McCrory.
- Gauss_map wikiPageWikiLink Cusp_(singularity).
- Gauss_map wikiPageWikiLink Degree_of_a_continuous_mapping.
- Gauss_map wikiPageWikiLink Differential_(calculus).
- Gauss_map wikiPageWikiLink Differential_(mathematics).
- Gauss_map wikiPageWikiLink Differential_geometry.
- Gauss_map wikiPageWikiLink Differential_geometry_of_surfaces.
- Gauss_map wikiPageWikiLink Euclidean_space.
- Gauss_map wikiPageWikiLink Euler_characteristic.
- Gauss_map wikiPageWikiLink Gaussian_curvature.
- Gauss_map wikiPageWikiLink Gauss–Bonnet_theorem.
- Gauss_map wikiPageWikiLink Grassmann_bundle.
- Gauss_map wikiPageWikiLink Grassmannian.
- Gauss_map wikiPageWikiLink Hypersurface.
- Gauss_map wikiPageWikiLink Jacobian_matrix_and_determinant.
- Gauss_map wikiPageWikiLink Link_(knot_theory).
- Gauss_map wikiPageWikiLink Linking_number.
- Gauss_map wikiPageWikiLink Orientability.
- Gauss_map wikiPageWikiLink Orientable.
- Gauss_map wikiPageWikiLink Parabolic_line.
- Gauss_map wikiPageWikiLink Ridge_(differential_geometry).
- Gauss_map wikiPageWikiLink Riemannian_manifold.
- Gauss_map wikiPageWikiLink Shape_operator.
- Gauss_map wikiPageWikiLink Sphere.
- Gauss_map wikiPageWikiLink Submanifold.
- Gauss_map wikiPageWikiLink Surface.
- Gauss_map wikiPageWikiLink Surface_integral.
- Gauss_map wikiPageWikiLink Tangent_bundle.
- Gauss_map wikiPageWikiLink Terence_Gaffney.
- Gauss_map wikiPageWikiLink Thomas_Banchoff.
- Gauss_map wikiPageWikiLink Topology.
- Gauss_map wikiPageWikiLink File:Gauss_map.svg.
- Gauss_map wikiPageWikiLinkText "Gauss Map".
- Gauss_map wikiPageWikiLinkText "Gauss map".
- Gauss_map hasPhotoCollection Gauss_map.
- Gauss_map title "Gauss Map".
- Gauss_map urlname "GaussMap".
- Gauss_map wikiPageUsesTemplate Template:About.
- Gauss_map wikiPageUsesTemplate Template:Chaos_theory.
- Gauss_map wikiPageUsesTemplate Template:MathWorld.
- Gauss_map wikiPageUsesTemplate Template:No_footnotes.
- Gauss_map subject Category:Carl_Friedrich_Gauss.
- Gauss_map subject Category:Differential_geometry.
- Gauss_map subject Category:Differential_geometry_of_surfaces.
- Gauss_map subject Category:Riemannian_geometry.
- Gauss_map subject Category:Surfaces.
- Gauss_map type Article.
- Gauss_map type Article.
- Gauss_map type Physic.
- Gauss_map type Surface.
- Gauss_map comment "In differential geometry, the Gauss map (named after Carl F. Gauss) maps a surface in Euclidean space R3 to the unit sphere S2. Namely, given a surface X lying in R3, the Gauss map is a continuous map N: X → S2 such that N(p) is a unit vector orthogonal to X at p, namely the normal vector to X at p.The Gauss map can be defined (globally) if and only if the surface is orientable, in which case its degree is half the Euler characteristic. The Gauss map can always be defined locally (i.e.".
- Gauss_map label "Gauss map".
- Gauss_map sameAs Gauß-Abbildung.
- Gauss_map sameAs Application_de_Gauss.
- Gauss_map sameAs Gauss-afbeelding.
- Gauss_map sameAs m.021bk7.
- Gauss_map sameAs Отображение_Гаусса.
- Gauss_map sameAs Q575710.
- Gauss_map sameAs Q575710.
- Gauss_map sameAs 高斯映射.
- Gauss_map wasDerivedFrom Gauss_map?oldid=676616243.
- Gauss_map depiction Gauss_map.svg.
- Gauss_map isPrimaryTopicOf Gauss_map.
