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

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2017
• Main Authors: Hung-Lin Chiu, Yen-Chang Huang, Sin-Hua Lai
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2017
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/148834
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: An Application of the Moving Frame Method to Integral Geometry in the Heisenberg Group / Hung-Lin Chiu, Yen-Chang Huang, Sin-Hua Lai // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 24 назв. — англ.

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 Crof...