Singularities of improper affine spheres and surfaces of constant Gaussian curvature

Singularities of improper affine spheres and surfaces of constant Gaussian curvature
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DOI：
10.1142/s0129167x06003485
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发表时间：
2005-02
期刊：
--
影响因子：
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通讯作者：
G. Ishikawa;Y. Machida
G. Ishikawa;Y. Machida
中科院分区：
其他
文献类型：
--
作者：
G. Ishikawa;Y. Machida

文献摘要

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从接触几何的角度研究了广义(抛物线)仿射球面方程，给出了方程及其对偶几何解中出现的奇异性的一般分类。我们还给出了常高斯曲率曲面和可展曲面的结果。特别地，我们证实了出现在这类曲面上的一般奇点只是尖边和锯尾。
We study the equation for improper (parabolic) affine spheres from the view point of contact geometry and provide the generic classification of singlarities appearing in geometric solutions to the equation as well as their duals. We also show the results for surfaces of constant Gaussian curvature and for developable surfaces. In particular we confirm that generic singularities appearing in such a surface are just cuspidal edges and awallowtails.