Letting [Formula: see text] be a compact [Formula: see text]-curve embedded in the Euclidean [Formula: see text]-space ([Formula: see text] means real analyticity), we consider a [Formula: see text]-cuspidal edge [Formula: see text] along [Formula: see text]. When [Formula: see text] is non-closed, in the authors’ previous works, the local existence of three distinct cuspidal edges along [Formula: see text] whose first fundamental forms coincide with that of [Formula: see text] was shown, under a certain reasonable assumption on [Formula: see text]. In this paper, if [Formula: see text] is closed, that is, [Formula: see text] is a knot, we show that there exist infinitely many cuspidal edges along [Formula: see text] having the same first fundamental form as that of [Formula: see text] such that their images are non-congruent to each other, in general.

中文翻译：

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沿结具有相同的第一基本形式的尖边

令 [Formula: see text] 是一个紧凑的 [Formula: see text]-curve 嵌入在 Euclidean [Formula: see text]-空间中（[Formula: see text] 表示真正的解析性），我们考虑一个 [Formula: see text] ]-尖边[公式：见正文]沿[公式：见正文]。[公式：见文]非闭合时，在作者之前的作品中，显示了沿[公式：见文]的三个明显尖边的局部存在，其第一基本形式与[公式：见文]的基本形式一致，在[公式：见正文]的某个合理假设下。在本文中，如果[公式：见文本]是封闭的，即[公式：见文本]是一个结，我们证明沿着[公式：见文本]存在无限多的尖边，具有相同的第一基本形式[公式：见文本]的图像，因此它们的图像彼此不一致，