Even Dimensional Improper Affine Spheres
Abstract
There are exactly two different types of bi-dimensional improper affine spheres: the non-convex ones can be modeled by the center-chord transform of a pair of planar curves while the convex ones can be modeled by a holomorphic map. In this paper, we show that both constructions can be generalized to arbitrary even dimensions: the former class corresponds to the center-chord transform of a pair of Lagrangian submanifolds while the latter is related to special K\"ahler manifolds. Furthermore, we show that the improper affine spheres obtained in this way are solutions of certain exterior differential systems. Finally, we also discuss the problem of realization of simple stable Legendrian singularities as singularities of these improper affine spheres.
Cite
@article{arxiv.1212.4722,
title = {Even Dimensional Improper Affine Spheres},
author = {Marcos Craizer and Wojciech Domitrz and Pedro de M. Rios},
journal= {arXiv preprint arXiv:1212.4722},
year = {2014}
}
Comments
26 pages