论文标题
海森伯格小组中帕普·古尔丁定理的概括
Generalizations of the theorems of Pappus-Guldin in the Heisenberg groups
论文作者
论文摘要
在本文中，我们研究了3D-Heisenberg $ \ Mathbb {H} _1 $中参数表面的区域（称为P-Areas）和体积，该区域被认为是伪 - 甲状化歧管的平坦模型。我们在$ \ mathbb {h} _1 $中得出了P-Areas的公式和参数表面的体积，并表明表面积的Pappus-Guldin定理的经典结果，如果表面满足某些几何特性，则体积保持。还提供了一些示例，包括具有恒定P均值曲率的表面。
In this paper we study areas (called p-areas) and volumes for parametric surfaces in the 3D-Heisenberg group $\mathbb{H}_1$, which is considered as a flat model of pseudo-hermitian manifolds. We derive the formulas of p-areas and volumes for parametric surfaces in $\mathbb{H}_1$ and show that the classical result of Pappus-Guldin theorems for surface areas and volumes hold if the surfaces satisfy some geometric properties. Some examples are also provided, including the surfaces with constant p-mean curvatures.
