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}
}
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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