Generalizations of the theorems of Pappus-Guldin in the Heisenberg groups

2020/01/14 by Huang, Yen-Chang
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2001.04578

Abstract

In this paper we study areas (called p-areas) and volumes for parametric surfaces in the 3D-Heisenberg group ℍ₁, which is considered as a flat model of pseudo-hermitian manifolds. We derive the formulas of p-areas and volumes for parametric surfaces in ℍ₁ 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.

Related

• Cauchy surface area formula in the Heisenberg groups
• Constant angle surfaces in the Heisenberg group
• A characterization of constant p-mean curvature surfaces in the Heisenberg group H₁
• Ruled surfaces of finite type in 3-dimensional Heisenberg group
• Area-stationary surfaces in the Heisenberg group H¹