An Application of the Moving Frame Method to Integral Geometry in the Heisenberg Group
Differential Geometry
2017-12-27 v3
Abstract
We show the fundamental theorems of curves and surfaces in the 3-dimensional Heisenberg group and find a complete set of invariants for curves and surfaces respectively. The proofs are based on Cartan's method of moving frames and Lie group theory. As an application of the main theorems, a Crofton-type formula is proved in terms of p-area which naturally arises from the variation of volume. The application makes a connection between CR geometry and integral geometry.
Keywords
Cite
@article{arxiv.1509.00950,
title = {An Application of the Moving Frame Method to Integral Geometry in the Heisenberg Group},
author = {Hung-Lin Chiu and Yen-Chang Huang and Sin-Hua Lai},
journal= {arXiv preprint arXiv:1509.00950},
year = {2017}
}