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Symmetry, Integrability and Geometry: Methods and Applications, 2017, Volume 13, 097, 27 pp.
DOI: https://doi.org/10.3842/SIGMA.2017.097 (Mi sigma1297) 		 
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
Full-text PDF (522 kB) Citations (6)
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DOI: https://doi.org/10.3842/SIGMA.2017.097
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.
Funding agency Grant number
Ministry of Science and Technology, Taiwan NSC-100-2628-M-008-001-MY4
The first and second authors’ research was supported by NCTS grant NSC-100-2628-M-008-001-MY4.
Received: March 9, 2017; in final form December 9, 2017; Published online December 26, 2017
Bibliographic databases:
Document Type: Article
MSC: 53C15; 53C65; 32V20
Language: English
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.
Citation in format AMSBIB
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    • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Symmetry, Integrability and Geometry: Methods and Applications
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