A nonlinear transformation between space curves defined by curvature-torsion relations in 3-dimensional Euclidean space

E. Öztürk
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Abstract

In this paper, we define a nonlinear transformation between space curves which preserves the ratio of $\tau/\kappa$ of the given curve in 3−dimensional Euclidean space $E^3$. We investigate invariant and associated curves of this transformation by the help of curvature and torsion functions of the base curve. Moreover, we define a new curve (family) so-called quasi-slant helix, and we obtain some characterizations in terms of the curvatures of this curve. Finally, we examine some curves in the kinematics, and give the pictures of some special curves and their images with respect to the transformation.
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三维欧氏空间中由曲率-扭转关系定义的空间曲线之间的非线性变换
在本文中,我们定义了一种空间曲线间的非线性变换,该变换保持了给定曲线在三维欧几里得空间$E^3$中的比值$\tau/\kappa$。利用基曲线的曲率函数和扭转函数研究了该变换的不变曲线和相关曲线。此外,我们定义了一种新的曲线(族),即所谓的拟斜螺旋,并得到了关于该曲线的曲率的一些表征。最后,我们考察了运动学中的一些曲线,并给出了一些特殊曲线的图像及其变换后的图像。
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