THE CENTER MAP OF AN AFFINE IMMERSION
Preprint Series # 665
FURUHATA, Hitoshi and VRANCKEN, Luc THE CENTER MAP OF AN AFFINE IMMERSION. (2004);
We study the center map of an equiaffine immersion
which is introduced using the equiaffine support function.
The center map is a constant map
if and only if the hypersurface is an equiaffine sphere.
We investigate those immersions
for which the center map is affine congruent with the original hypersurface.
In terms of centroaffine geometry,
we show that such hypersurfaces provide examples
of hypersurfaces with vanishing centroaffine Tchebychev operator.
We also characterize them in equiaffine differential geometry
using a curvature condition
involving the covariant derivative of the shape operator.
From both approaches, assuming the dimension is 2
and the surface is definite, a complete classification follows.
|Additional Information:||40 copies needed|
|Uncontrolled Keywords:||affine sphere, Tchebychev operator,
projectively flat affine surface|
|Subjects:||53-xx DIFFERENTIAL GEOMETRY|