The Cauchy problem for indefinite improper affine spheres and their Hessian equation |
| |
Authors: | Francisco Milá n |
| |
Affiliation: | Departamento de Geometría y Topología, Universidad de Granada, E-18071 Granada, Spain |
| |
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 geodesically complete non-flat affine metric. Moreover, we present interesting examples with singular curves and isolated singularities. |
| |
Keywords: | 53A15 |
本文献已被 ScienceDirect 等数据库收录! |
|