Dupin hypersurfaces (Q793340)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: Dupin hypersurfaces |
scientific article; zbMATH DE number 3855886
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Dupin hypersurfaces |
scientific article; zbMATH DE number 3855886 |
Statements
Dupin hypersurfaces (English)
0 references
1985
0 references
A surface in 3-space is a cyclide of Dupin if and only if along each line of curvature the corresponding principal curvature is constant. Accordingly a hypersurface in n-space is called a ''Dupin hypersurface'' if the principal curvatures are constant along the leaves of the corresponding curvature foliations. In this paper Dupin hypersurfaces are studied from the viewpoint of Lie-geometry. In particular several constructions are described that provide examples of Dupin hypersurfaces. Furthermore the Dupin hypersurfaces with only two distinct principal curvatures are completely classified.
0 references
principal curvature
0 references
Dupin hypersurface
0 references
Lie-geometry
0 references
