Relative Tchebychev hypersurfaces which are also translation hypersurfaces.
Hokkaido Mathematical Journal, 38 (2009) pp.97-110
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.
|Uncontrolled Keywords||Centroaffine geometry, relative geometry, Tchebychev hypersurfaces, translation hypersurfaces|