Dupin hypersurface information

geometry, a Dupin hypersurface is a submanifold in a space form, whose principal curvatures have globally constant multiplicities. A hypersurface is called...

Baron Pierre Charles François Dupin (French pronunciation: [pjɛʁ ʃaʁl fʁɑ̃swa dypɛ̃]; 6 October 1784, Varzy, Nièvre – 18 January 1873, Paris, France)...

planes) turns out to be a manifold known as the Lie quadric (a quadric hypersurface in projective space). Lie sphere geometry is the geometry of the Lie...

1979 and a doctorate in 1982 with thesis Dupin'sche Hyperflächen (Dupin's hypersurfaces) under the supervision of Martin Barner. Pinkall was then a research...

fundamental form Second fundamental form Gauss–Codazzi–Mainardi equations Dupin indicatrix Asymptotic curve Curvature Principal curvatures Mean curvature...

pencils of circles. The inversion of a cylinder, cone, or torus results in a Dupin cyclide. A spheroid is a surface of revolution and contains a pencil of...