# 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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