In this paper, we get the time evolution equations of the curvature and the torsion of a space-like curve in the three-dimensional Minkowski space. Also, we give inextensible evolutions of a time-like ruled surface that is produced by a time-like normal vector and a space-like binormal vector of a space-like curve and derive the necessary conditions for an inelastic surface evolution. As a result, we give applications of the time evolution equations for the curvature and the torsion of the space-like curve in terms of the velocities and get the exact solutions for these equations.

中文翻译：

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Minkowski空间中类似空间的曲线和特殊的类似时间的直纹曲面的演化

在本文中，我们获得了三维Minkowski空间中类空曲线的曲率和扭转的时间演化方程。另外，我们给出了由时空法线向量和时空曲线的时空双法线向量生成的时空直纹曲面的不可扩展的演化，并推导了非弹性曲面演化的必要条件。结果，我们给出了关于速度曲线的曲率和扭转的时间演化方程的应用，并获得了这些方程的精确解。