# An Application of the Moving Frame Method to Integral Geometry in the Heisenberg Group

```@article{Chiu2015AnAO,
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={Symmetry Integrability and Geometry-methods and Applications},
year={2015},
volume={13},
pages={097}
}```
• Published 3 September 2015
• Mathematics
• Symmetry Integrability and Geometry-methods and Applications
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.
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