In this work, we compute the time evolution equations (TEEs) of the type-1 Bishop frame of the curve. Also, we study the time evolution equations for type-1 Bishop curvatures (TEEBCs) as a system of partial differential equations (PDEs). Through this study, we give a necessary and sufficient condition for the normal and binormal Bishop velocities. Also, we construct new models of normal motions of inextensible curves in [Formula: see text]. These models are constructed for curves that move according to the type-1 Bishop frame. Also, we make a comparison study between surfaces obtained by the motions of inextensible curves according to the two frames, the type-1 Bishop frame and the Frenet frame.

中文翻译：

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ℝ3 中根据 type-1 Bishop 框架的不可伸曲线法向运动的新模型

在这项工作中，我们计算曲线的 1 型 Bishop 框架的时间演化方程 (TEE)。此外，我们将 1 型 Bishop 曲率 (TEEBC) 的时间演化方程作为偏微分方程 (PDE) 系统进行研究。通过这项研究，我们给出了正常和副正常 Bishop 速度的充要条件。此外，我们在 [公式：见正文] 中构建了不可延展曲线法向运动的新模型。这些模型是为根据类型 1 Bishop 框架移动的曲线构建的。此外，我们还根据第一类 Bishop 框架和 Frenet 框架两种框架对不可伸曲线运动得到的曲面进行了比较研究。