In this paper, we introduce a new class of curves that we call helical extension curve in Euclidean space. Then we investigate the differential geometric properties of the helical extension curves. The main result of the paper is that the helical extension curve of a helix is a plane curve. Moreover, we give several simple characterizations of helical extension curve of special curves such as spherical curve.

中文翻译：

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空间曲线的螺旋延伸曲线

在本文中，我们介绍了一类新的曲线，称为欧氏空间中的螺旋形延伸曲线。然后，我们研究了螺旋延伸曲线的微分几何特性。本文的主要结果是螺旋线的螺旋延伸曲线是平面曲线。此外，我们给出了特殊曲线（例如球形曲线）的螺旋延伸曲线的几个简单特征。