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- Hypersurface abstract "For differential geometry usage, see glossary of differential geometry and topology.In geometry, a hypersurface is a generalization of the concept of hyperplane. Suppose an enveloping manifold M has n dimensions; then any submanifold of M of n − 1 dimensions is a hypersurface. Equivalently, the codimension of a hypersurface is one. For example, the n-sphere in Rn + 1 is called a hypersphere. Hypersurfaces occur frequently in multivariable calculus as level sets.In Rn, every closed hypersurface is orientable.Every connected compact hypersurface is a level set, and separates Rn in two connected components, which is related to the Jordan–Brouwer separation theorem.In algebraic geometry, a hypersurface in projective space of dimension n is an algebraic set (algebraic variety) that is purely of dimension n − 1. It is then defined by a single equation f(x1,x2,...,xn) = 0, a homogeneous polynomial in the homogeneous coordinates.Thus, it generalizes those algebraic curves f(x1,x2) = 0 (dimension one), and those algebraic surfaces f(x1,x2,x3) = 0 (dimension two), when they are defined by homogeneous polynomials.A hypersurface may have singularities, so not a submanifold in the strict sense. \"Primal\" is an old term for an irreducible hypersurface.".
- Hypersurface thumbnail Ackley3.gif?width=300.
- Hypersurface wikiPageExternalLink s00371-004-0260-4.
- Hypersurface wikiPageID "525101".
- Hypersurface wikiPageLength "2925".
- Hypersurface wikiPageOutDegree "35".
- Hypersurface wikiPageRevisionID "646003098".
- Hypersurface wikiPageWikiLink Affine_sphere.
- Hypersurface wikiPageWikiLink Algebraic_curve.
- Hypersurface wikiPageWikiLink Algebraic_geometry.
- Hypersurface wikiPageWikiLink Algebraic_surface.
- Hypersurface wikiPageWikiLink Algebraic_variety.
- Hypersurface wikiPageWikiLink Category:Algebraic_geometry.
- Hypersurface wikiPageWikiLink Category:Multi-dimensional_geometry.
- Hypersurface wikiPageWikiLink Coble_hypersurface.
- Hypersurface wikiPageWikiLink Codimension.
- Hypersurface wikiPageWikiLink Differential_geometry.
- Hypersurface wikiPageWikiLink Dimension.
- Hypersurface wikiPageWikiLink Dwork_family.
- Hypersurface wikiPageWikiLink Foundations_of_Differential_Geometry.
- Hypersurface wikiPageWikiLink Geometry.
- Hypersurface wikiPageWikiLink Glossary_of_differential_geometry_and_topology.
- Hypersurface wikiPageWikiLink Homogeneous_coordinates.
- Hypersurface wikiPageWikiLink Homogeneous_polynomial.
- Hypersurface wikiPageWikiLink Hyperplane.
- Hypersurface wikiPageWikiLink John_Wiley_&_Sons.
- Hypersurface wikiPageWikiLink Jordan_curve_theorem.
- Hypersurface wikiPageWikiLink Katsumi_Nomizu.
- Hypersurface wikiPageWikiLink Level_set.
- Hypersurface wikiPageWikiLink Manifold.
- Hypersurface wikiPageWikiLink Multivariable_calculus.
- Hypersurface wikiPageWikiLink N-sphere.
- Hypersurface wikiPageWikiLink Null_hypersurface.
- Hypersurface wikiPageWikiLink Orientability.
- Hypersurface wikiPageWikiLink Polar_hypersurface.
- Hypersurface wikiPageWikiLink Projective_space.
- Hypersurface wikiPageWikiLink Shoshichi_Kobayashi.
- Hypersurface wikiPageWikiLink Singularity_(mathematics).
- Hypersurface wikiPageWikiLink Submanifold.
- Hypersurface wikiPageWikiLink Test_functions_for_optimization.
- Hypersurface wikiPageWikiLink File:Ackley3.gif.
- Hypersurface wikiPageWikiLinkText "(hyper-)surface".
- Hypersurface wikiPageWikiLinkText "Hypersurface".
- Hypersurface wikiPageWikiLinkText "hypersurface".
- Hypersurface wikiPageWikiLinkText "surface".
- Hypersurface id "H/h048520".
- Hypersurface title "Hypersurface".
- Hypersurface wikiPageUsesTemplate Template:Reflist.
- Hypersurface wikiPageUsesTemplate Template:Springer.
- Hypersurface subject Category:Algebraic_geometry.
- Hypersurface subject Category:Multi-dimensional_geometry.
- Hypersurface hypernym Generalization.
- Hypersurface comment "For differential geometry usage, see glossary of differential geometry and topology.In geometry, a hypersurface is a generalization of the concept of hyperplane. Suppose an enveloping manifold M has n dimensions; then any submanifold of M of n − 1 dimensions is a hypersurface. Equivalently, the codimension of a hypersurface is one. For example, the n-sphere in Rn + 1 is called a hypersphere.".
- Hypersurface label "Hypersurface".
- Hypersurface sameAs Q973321.
- Hypersurface sameAs Hyperfläche.
- Hypersurface sameAs Hipersuperficie.
- Hypersurface sameAs Hypersurface.
- Hypersurface sameAs ऊनविम_पृष्ठ.
- Hypersurface sameAs Ipersuperficie.
- Hypersurface sameAs 超曲面.
- Hypersurface sameAs Гипербет.
- Hypersurface sameAs Хиперповршина.
- Hypersurface sameAs Hyperoppervlak.
- Hypersurface sameAs Hipersuperfície.
- Hypersurface sameAs m.0117bj5v.
- Hypersurface sameAs Гиперповерхность.
- Hypersurface sameAs Hiperploskev.
- Hypersurface sameAs Q973321.
- Hypersurface sameAs 超曲面.
- Hypersurface wasDerivedFrom Hypersurface?oldid=646003098.
- Hypersurface depiction Ackley3.gif.
- Hypersurface isPrimaryTopicOf Hypersurface.