Hokkaido Mathematical Journal

Relative Tchebychev hypersurfaces which are also translation hypersurfaces

Thomas BINDER

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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.

Article information

Source
Hokkaido Math. J., Volume 38, Number 1 (2009), 97-110.

Dates
First available in Project Euclid: 28 July 2009

Permanent link to this document
https://projecteuclid.org/euclid.hokmj/1248787014

Digital Object Identifier
doi:10.14492/hokmj/1248787014

Mathematical Reviews number (MathSciNet)
MR2501896

Zentralblatt MATH identifier
1180.53011

Subjects
Primary: 53A15: Affine differential geometry

Keywords
Centroaffine geometry relative geometry Tchebychev hypersurfaces translation hypersurfaces

Citation

BINDER, Thomas. Relative Tchebychev hypersurfaces which are also translation hypersurfaces. Hokkaido Math. J. 38 (2009), no. 1, 97--110. doi:10.14492/hokmj/1248787014. https://projecteuclid.org/euclid.hokmj/1248787014


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