Constant mean curvature tori in terms of elliptic functions.
Constant mean curvature tori in terms of elliptic functions.
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用椭圆函数表示的恒定平均曲率环面。
DOI：
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发表时间：
1987
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通讯作者：
U. Abresch
中科院分区：
文献类型：
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作者：
U. Abresch
基于这种解的数值近似，我们可以产生一个f-环面的曲线图。在这些计算机生成的图片中，较小的主曲率λ^的曲率线看起来几乎是平面的。然后我们决定将自己限制在只有一族平面曲率线的fftori上。这个条件转化为第二个偏微分方程导出了Sinh-Gordon方程中的变量分离。因此，超定系统可以用椭圆函数显式求解。我们得到了E中所有有一族平面曲率线族的f-环面的分类。
Based on a numerical approximation of such a solution, we could produce plots of one ff-torus. In these Computer generated pictures the curvature lines for the smaller principal curvature λ^ looked almost planar. We then decided to restrict ourselves to fftori with one family of planar curvature lines. This condition translates into a second partial differential equation which induces a Separation of variables in the sinh-Gordon equation. Therefore the overdetermined System can be solved explicitly in terms of elliptic functions. We obtain a classification of all ff-tori in E which have one family of planar curvature lines.