沿纽结具有相同第一基本型的尖棱
Cuspidal edges with the same first fundamental forms along a knot
摘要：
设$C$是嵌入$\boldsymbol R^3$的紧致$C^ω$ -曲线（$C^ω$表示实解析性），我们考虑沿$C$的$C^ω$ -尖点边$f$.在对$f$的合理假设下，证明了当$C$为非闭时，$C$上局部存在三条尖边，它们的第一基本型与$f$的第一基本型一致.在本文中，如果$C$是封闭的，也就是说，$C$是一个纽结，我们证明了存在无穷多个尖点边缘沿$C$具有相同的第一基本型的$f$，使他们的图像是不全等，在一般情况下。
英文摘要：
Letting $C$ be a compact $C^ω$-curve embedded in $\boldsymbol R^3$ ($C^ω$ means real analyticity), we consider a $C^ω$-cuspidal edge $f$ along $C$. When $C$ is non-closed, in the authors' previous works, the local existence of three distinct cuspidal edges along $C$ whose first fundamental forms coincide with that of $f$ was shown, under a certain reasonable assumption on $f$. In this paper, if $C$ is closed, that is, $C$ is a knot, we show that there exist infinitely many cuspidal edges along $C$ having the same first fundamental form as that of $f$ such that their images are non-congruent to each other, in general.
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