Article ID Journal Published Year Pages File Type
4665881 Advances in Mathematics 2014 13 Pages PDF
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.

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Related Topics
Physical Sciences and Engineering Mathematics Mathematics (General)
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