Generalizations of the theorems of Pappus-Guldin in the Heisenberg groups (Q1979239)

In this paper, the author studies 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. The author derives the formulas of p-areas and volumes for parametric surfaces in \(\mathbb{H}^1\) and shows 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.