Hung-Lin Chiu, Yen-Chang Huang, Sin-Hua Lai, “An Application of the Moving Frame Method to Integral Geometry in the Heisenberg Group”, SIGMA, 2017, Volume 13,097, 27 pp.

This article is cited in 6 papers

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

Hung-Lin Chiu^a, Yen-Chang Huang^b, Sin-Hua Lai^a

^a Department of Mathematics, National Central University, Chung Li, Taiwan
^b School of Mathematics and Statistics, Xinyang Normal University, Henan, P.R. China

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.

Keywords: CR manifolds; Heisenberg groups; moving frames.

MSC: 53C15; 53C65; 32V20

Received: March 9, 2017; in final form December 9, 2017; Published online December 26, 2017

Language: English

DOI: 10.3842/SIGMA.2017.097