In this paper, we consider the curves on the surface in the unit 3-sphere. For a regular curve on a surface in the unit 3-sphere, we have a moving frame along the curve which is called a spherical Darboux frame. We induce two special vector fields along the curve with respect to the spherical Darboux frame and investigate the singularities of extrinsic flat great circular surfaces associated with these vector fields.

中文翻译：

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外球面在单元三球体中沿着曲面的曲线

在本文中，我们考虑单位3球体表面上的曲线。对于单位3球面上的规则曲线，我们沿该曲线有一个移动框架，称为球形达布斯框架。我们沿曲线相对于球形Darboux框架推导了两个特殊的矢量场，并研究了与这些矢量场相关的外在平坦大圆形表面的奇异性。