Ghomi 和 Raffaelli 关于闭渐近曲线问题的解
A solution to a problem of Ghomi and Raffaelli on closed asymptotic curves
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中文总结 AI 辅助
本文构造了具有严格负高斯曲率和单射高斯映射的嵌入开环带，其中包含法向自链数为零的闭渐近曲线，从而肯定解决了 Ghomi 和 Raffaelli 的问题 1.1。
中文摘要 AI 辅助
我们在欧几里得三维空间中构造了一个光滑嵌入的开环带，其高斯曲率严格为负，且高斯映射为单射，该环带包含一条法向自链数为零的简单闭渐近曲线。这为 Ghomi 和 Raffaelli 的问题 1.1 给出了肯定回答。构造始于两条简单平面曲线，它们的切向量互为正倍数。通过舍入一对具有一个自由长度参数的多边形，使其混合积为零。
英文摘要
We construct a smooth embedded open annulus in Euclidean three-space with strictly negative Gaussian curvature and injective Gauss map that contains a simple closed asymptotic curve of zero normal self-linking. This gives an affirmative answer to Problem 1.1 of Ghomi and Raffaelli. The construction starts with two simple planar curves whose tangent vectors are positive multiples of one another. Their mixed integral is made zero by rounding a pair of polygons with one free length parameter.
发表机构
- School of Mathematical Sciences, South China Normal University（华南师范大学数学科学学院）
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