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Improper affine spheres in ℝ3 and ℂ3

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Abstract

In this paper we determined all polynomial improper affine spheres in ℝ3 and ℂ3 without any curvature conditions. We have gotten the following result: A polynomial improper affine sphere in ℝ3 or ℂ3 is either a quadric or the ruled surface z = xy +ϕ(x).

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  1. Department of Mathematics and Statistics, Southern Illinois University at Edwardsville, Edwardsville, IL 62026-1653, USA

    Weiqi Gao

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  1. Weiqi Gao
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Gao, W. Improper affine spheres in ℝ3 and ℂ3 . Results. Math. 24, 222–227 (1993). https://doi.org/10.1007/BF03322332

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  • DOI: https://doi.org/10.1007/BF03322332

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