An Application of the Moving Frame Method to Integral Geometry in the Heisenberg Group
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...
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| Видавець: | Інститут математики НАН України |
|---|---|
| Дата: | 2017 |
| Автори: | , , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2017
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/148834 |
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| Цитувати: | 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. |
Репозиторії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-148834 |
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dspace |
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irk-123456789-1488342019-02-19T01:23:59Z An Application of the Moving Frame Method to Integral Geometry in the Heisenberg Group Hung-Lin Chiu Yen-Chang Huang Sin-Hua Lai 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. 2017 Article 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. 1815-0659 2010 Mathematics Subject Classification: 53C15; 53C65; 32V20 DOI:10.3842/SIGMA.2017.097 http://dspace.nbuv.gov.ua/handle/123456789/148834 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
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. |
| format |
Article |
| author |
Hung-Lin Chiu Yen-Chang Huang Sin-Hua Lai |
| spellingShingle |
Hung-Lin Chiu Yen-Chang Huang Sin-Hua Lai An Application of the Moving Frame Method to Integral Geometry in the Heisenberg Group Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Hung-Lin Chiu Yen-Chang Huang Sin-Hua Lai |
| author_sort |
Hung-Lin Chiu |
| title |
An Application of the Moving Frame Method to Integral Geometry in the Heisenberg Group |
| title_short |
An Application of the Moving Frame Method to Integral Geometry in the Heisenberg Group |
| title_full |
An Application of the Moving Frame Method to Integral Geometry in the Heisenberg Group |
| title_fullStr |
An Application of the Moving Frame Method to Integral Geometry in the Heisenberg Group |
| title_full_unstemmed |
An Application of the Moving Frame Method to Integral Geometry in the Heisenberg Group |
| title_sort |
application of the moving frame method to integral geometry in the heisenberg group |
| publisher |
Інститут математики НАН України |
| publishDate |
2017 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/148834 |
| citation_txt |
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. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT hunglinchiu anapplicationofthemovingframemethodtointegralgeometryintheheisenberggroup AT yenchanghuang anapplicationofthemovingframemethodtointegralgeometryintheheisenberggroup AT sinhualai anapplicationofthemovingframemethodtointegralgeometryintheheisenberggroup AT hunglinchiu applicationofthemovingframemethodtointegralgeometryintheheisenberggroup AT yenchanghuang applicationofthemovingframemethodtointegralgeometryintheheisenberggroup AT sinhualai applicationofthemovingframemethodtointegralgeometryintheheisenberggroup |
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2023-05-20T17:31:28Z |
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2023-05-20T17:31:28Z |
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1796153488181297152 |