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Geometriae Dedicata

, Volume 66, Issue 2, pp 203–221 | Cite as

Cubic Form Methods and Relative Tchebychev Hypersurfaces

  • A.-M. LI
  • H. L. LIU
  • A. SCHWENK-SCHELLSCHMIDT
  • U. SIMON
  • C. P. WANG
Article

Abstract

We introduce the concept of a relative Tchebychev hypersurface which extends that of affine spheres in equiaffine geometry and also that of centroaffine Tchebychev hypersurfaces and give partial local and global classifications for this new class. Our tools concern a new operator and interesting properties of the traceless part of the cubic form.

Tchebychev hypersurface relative geometry hyperovaloid cubic form. 

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Copyright information

© Kluwer Academic Publishers 1997

Authors and Affiliations

  • A.-M. LI
    • 1
  • H. L. LIU
    • 2
  • A. SCHWENK-SCHELLSCHMIDT
    • 3
  • U. SIMON
    • 2
  • C. P. WANG
    • 2
  1. 1.Department of MathematicsSichuna UniversityChengduP.R. China
  2. 2.FB3-MathematikTechnische Universität BerlinBerlinGermany
  3. 3.FB2-Mathematik/PhysikTechnische Fachhochschule BerlinBerlinGermany

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