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- Enneper_surface abstract "In mathematics, in the fields of differential geometry and algebraic geometry, the Enneper surface is a self-intersecting surface that can be described parametrically by: It was introduced by Alfred Enneper 1864 in connection with minimal surface theory.The Weierstrass–Enneper parameterization is very simple, , and the real parametric form can easily be calculated from it. The surface is conjugate to itself.Implicitization methods of algebraic geometry can be used to find out that the points in the Enneper surface given above satisfy the degree-9 polynomial equation Dually, the tangent plane at the point with given parameters is where Its coefficients satisfy the implicit degree-6 polynomial equation The Jacobian, Gaussian curvature and mean curvature are The total curvature is . Osserman proved that a complete minimal surface in with total curvature is either the catenoid or the Enneper surface.Another property is that all bicubical minimal Bézier surfaces are, up to an affine transformation, pieces of the surface.It can be generalized to higher order rotational symmetries by using the Weierstrass–Enneper parameterization for integer k>1. It can also be generalized to higher dimensions; Enneper-like surfaces are known to exist in for n up to 7.".
- Enneper_surface thumbnail EnneperSurfaceAnimated.gif?width=300.
- Enneper_surface wikiPageExternalLink enneper.html.
- Enneper_surface wikiPageExternalLink index.html.
- Enneper_surface wikiPageID "4688830".
- Enneper_surface wikiPageRevisionID "575990663".
- Enneper_surface hasPhotoCollection Enneper_surface.
- Enneper_surface id "p/e035710".
- Enneper_surface title "Enneper surface".
- Enneper_surface subject Category:Algebraic_geometry.
- Enneper_surface subject Category:Algebraic_surfaces.
- Enneper_surface subject Category:Minimal_surfaces.
- Enneper_surface type AlgebraicSurfaces.
- Enneper_surface type Artifact100021939.
- Enneper_surface type MinimalSurfaces.
- Enneper_surface type Object100002684.
- Enneper_surface type PhysicalEntity100001930.
- Enneper_surface type Surface104362025.
- Enneper_surface type Whole100003553.
- Enneper_surface comment "In mathematics, in the fields of differential geometry and algebraic geometry, the Enneper surface is a self-intersecting surface that can be described parametrically by: It was introduced by Alfred Enneper 1864 in connection with minimal surface theory.The Weierstrass–Enneper parameterization is very simple, , and the real parametric form can easily be calculated from it.".
- Enneper_surface label "Enneper surface".
- Enneper_surface label "Enneper-oppervlak".
- Enneper_surface label "Superficie di Enneper".
- Enneper_surface label "Surface d'Enneper".
- Enneper_surface sameAs Surface_d'Enneper.
- Enneper_surface sameAs Superficie_di_Enneper.
- Enneper_surface sameAs Enneper-oppervlak.
- Enneper_surface sameAs m.0chfxy.
- Enneper_surface sameAs Q615502.
- Enneper_surface sameAs Q615502.
- Enneper_surface sameAs Enneper_surface.
- Enneper_surface wasDerivedFrom Enneper_surface?oldid=575990663.
- Enneper_surface depiction EnneperSurfaceAnimated.gif.
- Enneper_surface isPrimaryTopicOf Enneper_surface.
