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