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arXiv · 1509.00950

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

Hung-Lin Chiu·Yen-Chang Huang·Sin-Hua Lai
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Abstract

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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Hung-Lin Chiu, Yen-Chang Huang, Sin-Hua Lai. 2015-09-03. An Application of the Moving Frame Method to Integral Geometry in the Heisenberg Group. https://doi.org/10.3842/sigma.2017.097

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