论文标题
Cesáro的条件，用于平坦的伪曲片中的曲线
Cesáro condition for curves in the flat pseudo-hermitian manifolds
论文作者
论文摘要
通过将三维Heisenberg组$ \ Mathbb {H} _1 $作为伪 - - 雷米特歧管的平坦模型，[8]中的作者得出了frenet-serret公式的曲线，以$ \ m m i \ m mathbb {h} _1 $ $。在此注释中，我们显示了Frenet-Serret公式的三个应用。首先是Cesáro固定条件，该条件提供了在给定的旋转对称表面中包含的曲线标准。其次，我们表明任何水平的规则曲线都是Bertrand曲线，并给出这些曲线的所有特征。最终应用是曲线的分类，具体取决于曲线的位置向量是否位于其任何对单位切线，正常和二手矢量跨越的平面上。
By considering the three dimensional Heisenberg group $\mathbb{H}_1$ as a flat model of pseudo-hermitian manifolds, the authors in [8] derived the Frenet-Serret formulas for curves in $\mathbb{H}_1$. In this notes we show three applications of the Frenet-Serret formulas. The first is the Cesáro immobility condition, which provides the criterion of curves being contained in a given rotationally symmetric surface. Secondly, we show that any horizontally regular curve is a Bertrand curve, and give all characterizations of those curves. The final application is a classification of curves depending on whether the position vector of the curve lies on the planes spanned by any pair of its unit tangent, normal, and binormal vectors.
