In this paper, we present a theorem which explains the necessary onditions for parallel surfaces of null scrolls to be surfaces again. Then, we give some properties of parallel ruled surfaces such as the frame fields in terms of the original base curve’s frame vectors, the cases of cross products of these frames’ vector fields. Also, we show the parallel ruled surfaces to be developable from a different point of view. Additionally, we obtain a relation between Gauss curvatures and mean curvatures. Finally, we characterize the striction curve of the parallel ruled surface. In the example, we draw a graph for a particular null scroll and its parallel surface.

中文翻译：

---

零卷轴作为平行表面的新特征

在本文中，我们提出了一个定理，该定理解释了空卷轴的平行表面再次成为表面的必要条件。然后，我们给出了平行直纹面的一些性质，例如原始基曲线的框架向量的框架场，这些框架向量场的叉积的情况。此外，我们展示了平行直纹面可以从不同的角度展开。此外，我们获得了高斯曲率和平均曲率之间的关系。最后，我们表征了平行直纹面的严格曲线。在示例中，我们为特定的空滚动及其平行表面绘制图形。