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This article is cited in 6 scientific papers (total in 6 papers)
An Application of the Moving Frame Method to Integral Geometry in the Heisenberg Group
Hung-Lin Chiua, Yen-Chang Huangb, Sin-Hua Laia 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.
Received: March 9, 2017; in final form December 9, 2017; Published online December 26, 2017
Citation:
Hung-Lin Chiu, Yen-Chang Huang, Sin-Hua Lai, “An Application of the Moving Frame Method to Integral Geometry in the Heisenberg Group”, SIGMA, 13 (2017), 097, 27 pp.
Linking options:
https://www.mathnet.ru/eng/sigma1297 https://www.mathnet.ru/eng/sigma/v13/p97
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Abstract page: | 466 | Full-text PDF : | 38 | References: | 20 |
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