Analytic formulas for complete hyperbolic affine spheres
Differential Geometry
2013-05-22 v1
Abstract
We classify all regular three-dimensional convex cones which possess an automorphism group of dimension at least two, and provide analytic expressions for the complete hyperbolic affine spheres which are asymptotic to the boundaries of these cones. The affine spheres are represented by explicit hypersurface immersions into three-dimensional real space. The generic member of the family of immersions is given by elliptic integrals.
Cite
@article{arxiv.1305.4814,
title = {Analytic formulas for complete hyperbolic affine spheres},
author = {Roland Hildebrand},
journal= {arXiv preprint arXiv:1305.4814},
year = {2013}
}
Comments
16 pages