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...
Gespeichert in:
| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Datum: | 2017 |
| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Інститут математики НАН України
2017
|
| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/148834 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | 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. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862730927640150016 |
|---|---|
| author | Hung-Lin Chiu Yen-Chang Huang Sin-Hua Lai |
| author_facet | Hung-Lin Chiu Yen-Chang Huang Sin-Hua Lai |
| 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. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| 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.
|
| first_indexed | 2025-12-07T19:23:52Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-148834 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T19:23:52Z |
| publishDate | 2017 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Hung-Lin Chiu Yen-Chang Huang Sin-Hua Lai 2019-02-18T19:57:59Z 2019-02-18T19:57:59Z 2017 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 https://nasplib.isofts.kiev.ua/handle/123456789/148834 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. 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. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications An Application of the Moving Frame Method to Integral Geometry in the Heisenberg Group Article published earlier |
| spellingShingle | An Application of the Moving Frame Method to Integral Geometry in the Heisenberg Group Hung-Lin Chiu Yen-Chang Huang Sin-Hua Lai |
| title | 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_short | 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 |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/148834 |
| work_keys_str_mv | AT hunglinchiu anapplicationofthemovingframemethodtointegralgeometryintheheisenberggroup AT yenchanghuang anapplicationofthemovingframemethodtointegralgeometryintheheisenberggroup AT sinhualai anapplicationofthemovingframemethodtointegralgeometryintheheisenberggroup AT hunglinchiu applicationofthemovingframemethodtointegralgeometryintheheisenberggroup AT yenchanghuang applicationofthemovingframemethodtointegralgeometryintheheisenberggroup AT sinhualai applicationofthemovingframemethodtointegralgeometryintheheisenberggroup |