The Cauchy problem for indefinite improper affine spheres and their Hessian equation
classification
🧮 math.DG
keywords
affineimproperindefinitespherescauchyequationhessianproblem
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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.
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