Invariance groups of relative normals
Volume 69 / 2005
Banach Center Publications 69 (2005), 171-178
MSC: Primary 53A15; Secondary 53A10.
DOI: 10.4064/bc69-0-12
Abstract
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.
