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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc69-0-12,
author = {Thomas Binder and Martin Wiehe},
title = {Invariance groups of relative normals},
journal = {Banach Center Publications},
volume = {68},
year = {2005},
pages = {171-178},
zbl = {1089.53009},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc69-0-12}
}
Thomas Binder; Martin Wiehe. Invariance groups of relative normals. Banach Center Publications, Tome 68 (2005) pp. 171-178. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc69-0-12/