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An Application of the Moving Frame Method to Integral Geometry in the Heisenberg Group
Symmetry, integrability and geometry: methods and applications, Tome 13 (2017) Cet article a éte moissonné depuis la source Math-Net.Ru

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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: CR manifolds; Heisenberg groups; moving frames. 
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Hung-Lin Chiu; Yen-Chang Huang; Sin-Hua Lai. An Application of the Moving Frame Method to Integral Geometry in the Heisenberg Group. Symmetry, integrability and geometry: methods and applications, Tome 13 (2017). http://geodesic.mathdoc.fr/item/SIGMA_2017_13_a96/

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