English

The Cauchy problem for indefinite improper affine spheres and their Hessian equation

Differential Geometry 2013-04-12 v2

Abstract

We give a conformal representation for indefinite improper affine spheres which solve the Cauchy problem for their Hessian equation. As consequences, we can characterize their geodesics and obtain a generalized symmetry principle. Then, we classify the helicoidal indefinite improper affine spheres and find a new family with complete non flat affine metric. Moreover, we present interesting examples with singular curves and isolated singularities.

Keywords

Cite

@article{arxiv.1302.5550,
  title  = {The Cauchy problem for indefinite improper affine spheres and their Hessian equation},
  author = {Francisco Milán},
  journal= {arXiv preprint arXiv:1302.5550},
  year   = {2013}
}