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An Application of the Moving Frame Method to Integral Geometry in the Heisenberg Group
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2017, том 13
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An Application of the Moving Frame Method to Integral Geometry in the Heisenberg Group
Інший ID:
2010 Mathematics Subject Classification: 53C15; 53C65; 32V20
DOI:10.3842/SIGMA.2017.097
DOI:10.3842/SIGMA.2017.097
Посилання:
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.
Підтримка:
The first and second authors’ research was supported by NCTS grant NSC-100-2628-M-008-
001-MY4. They would like to express their appreciation to Professors Jih-Hsin Cheng and Paul
Yang for their interests in this work and inspiring discussions. The third author would like to
express her thanks to Professor Shu-Cheng Chang for his teaching, constant encouragement,
and support. We all thank the anonymous referees for their careful reading of our manuscript
and their many insightful comments and suggestions to improve the paper.
Дата:
2017
Переглядів:
658
Завантажень:
273
Анотація:
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.
