论文标题
在$ \ mathbb {r}^n $中的曲线和试管上
ON CURVES AND TUBES IN $\mathbb{R}^n$
论文作者
论文摘要
在本文中，我们为欧几里得空间中的常规曲线的曲率提出了一个新的显式公式，$ \ mathbb {r}^n $，$ n \ geq 2 $仅以其衍生物表示。我们还介绍了管子的概念，该曲线围绕曲线进行任意横截面，我们为其计算体积并对Pappus的第二个定理进行概括。 Pappus的第一个定理是在任意维度的球体管中获得的。
In this paper, we present a new explicit formula for the curvatures of a regular curve with an arbitrary parameter in the Euclidean space $\mathbb{R}^n$, $n\geq 2$, expressed only in terms of its derivatives. We introduce also the notion of tube with arbitrary cross sections around a curve for which we calculate the volume and give a generalization for the second theorem of Pappus. The first theorem of Pappus is obtained for sphere tubes in arbitrary dimension.
