平面参数化曲线的流动曲率

IF 0.7 Q2 MATHEMATICS

Communications Faculty of Sciences University of Ankara-Series A1 Mathematics and Statistics Pub Date : 2023-06-23 DOI:10.31801/cfsuasmas.1165123

M. Crasmareanu

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引用次数: 0

摘要

我们介绍并研究了平面曲线固定参数化的一个新框架和一个新的曲率函数。这个新的框架被称为流动，因为它涉及到通常Frenet流动的时间相关旋转；旋转角度正是当前参数。计算了几个例子的流量曲率，获得了对数螺旋（和圆作为极限情况）和Grim Reaper作为平面流量曲线。主要结果是Frenet和flow框架的$\frac｛1｝｛\sqrt｛2｝｝$缩放属于Hopf丛的同一光纤。此外，定义并研究了流的费米-沃克导数。

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The flow-curvature of plane parametrized curves

We introduce and study a new frame and a new curvature function for a fixed parametrization of a plane curve. This new frame is called flow since it involves the time-dependent rotation of the usual Frenet flow; the angle of rotation is exactly the current parameter. The flow-curvature is calculated for several examples obtaining the logarithmic spirals (and the circle as limit case) and the Grim Reaper as flat-flow curves. A main result is that the scaling with$\frac{1}{\sqrt{2}}$ of both Frenet and flow-frame belong to the same fiber of the Hopf bundle. Moreover, the flow-Fermi-Walker derivative is defined and studied.

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Communications Faculty of Sciences University of Ankara-Series A1 Mathematics and Statistics MATHEMATICS-

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