Hokkaido Mathematical Journal

BINDER Thomas,

Relative Tchebychev hypersurfaces which are also translation hypersurfaces.

Hokkaido Mathematical Journal, 38 (2009) pp.97-110

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Abstract

The class of relative Tchebychev hypersurfaces extends the class of affine hyperspheres in Blaschke geometry. This paper aims at finding examples for relative Tchebychev hypersurfaces among the translation hypersurfaces. A complete local classification is given. Specializing from relative to centroaffine geometry, the list reduces to paraboloids.

MSC(Primary)53A15
MSC(Secondary)
Uncontrolled KeywordsCentroaffine geometry, relative geometry, Tchebychev hypersurfaces, translation hypersurfaces