Invariance groups of relative normals

Tom 69 / 2005

Thomas Binder, Martin Wiehe Banach Center Publications 69 (2005), 171-178 MSC: Primary 53A15; Secondary 53A10. DOI: 10.4064/bc69-0-12


We investigate a two-parameter family of relative normals that contains Manhart's one-parameter family and the centroaffine normal. The invariance group of each of these normals is classified, and variational problems are studied. The results are Euler-Lagrange equations for the hypersurfaces that are critical with respect to the area functionals of the induced and semi-Riemannian volume forms and a classification of the critical hyperovaloids in the two-parameter family.


  • Thomas BinderInstitute for Neuro- and Bioinformatics
    University of Lübeck
    Ratzeburger Allee 160
    D-23538 Lübeck, Germany
  • Martin WieheInstitute for Mathematics
    Technische Universität Berlin
    Strasse des 17. Juni 136
    D-10623 Berlin, Germany

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