Prolongation of (8, 15)-Distribution of Type ₄ by Singular Curves
Cartan gives the model of (8, 15)-distribution with the exceptional simple Lie algebra ₄ as its symmetry algebra in his paper (1893), which was published one year before his thesis. In the present paper, we study abnormal extremals (singular curves) of Cartan's model from the viewpoints of sub-...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2025 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2025
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/214092 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Prolongation of (8, 15)-Distribution of Type ₄ by Singular Curves. Goo Ishikawa and Yoshinori Machida. SIGMA 21 (2025), 076, 20 pages |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862650532244488192 |
|---|---|
| author | Ishikawa, Goo Machida, Yoshinori |
| author_facet | Ishikawa, Goo Machida, Yoshinori |
| citation_txt | Prolongation of (8, 15)-Distribution of Type ₄ by Singular Curves. Goo Ishikawa and Yoshinori Machida. SIGMA 21 (2025), 076, 20 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | Cartan gives the model of (8, 15)-distribution with the exceptional simple Lie algebra ₄ as its symmetry algebra in his paper (1893), which was published one year before his thesis. In the present paper, we study abnormal extremals (singular curves) of Cartan's model from the viewpoints of sub-Riemannian geometry and geometric control theory. Then we construct the prolongation of Cartan's model based on the data related to its singular curves, and obtain the nilpotent graded Lie algebra which is isomorphic to the negative part of the graded Lie algebra ₄.
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| first_indexed | 2026-03-15T15:00:09Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-214092 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-15T15:00:09Z |
| publishDate | 2025 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Ishikawa, Goo Machida, Yoshinori 2026-02-19T11:10:55Z 2025 Prolongation of (8, 15)-Distribution of Type ₄ by Singular Curves. Goo Ishikawa and Yoshinori Machida. SIGMA 21 (2025), 076, 20 pages 1815-0659 2020 Mathematics Subject Classification: 53C17; 58A30; 17B25; 34H05; 37J37; 49K15; 53D25 arXiv:2501.02789 https://nasplib.isofts.kiev.ua/handle/123456789/214092 https://doi.org/10.3842/SIGMA.2025.076 Cartan gives the model of (8, 15)-distribution with the exceptional simple Lie algebra ₄ as its symmetry algebra in his paper (1893), which was published one year before his thesis. In the present paper, we study abnormal extremals (singular curves) of Cartan's model from the viewpoints of sub-Riemannian geometry and geometric control theory. Then we construct the prolongation of Cartan's model based on the data related to its singular curves, and obtain the nilpotent graded Lie algebra which is isomorphic to the negative part of the graded Lie algebra ₄. The authors would like to thank anonymous referees for their valuable and helpful comments to improve the paper. The first author is partially supported by JSPS KAKENHI Grant Number 24K06700, by JST CREST Geometrical Understanding of Spatial Orientation, and by the Research Institute for Mathematical Sciences in Kyoto University. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Prolongation of (8, 15)-Distribution of Type ₄ by Singular Curves Article published earlier |
| spellingShingle | Prolongation of (8, 15)-Distribution of Type ₄ by Singular Curves Ishikawa, Goo Machida, Yoshinori |
| title | Prolongation of (8, 15)-Distribution of Type ₄ by Singular Curves |
| title_full | Prolongation of (8, 15)-Distribution of Type ₄ by Singular Curves |
| title_fullStr | Prolongation of (8, 15)-Distribution of Type ₄ by Singular Curves |
| title_full_unstemmed | Prolongation of (8, 15)-Distribution of Type ₄ by Singular Curves |
| title_short | Prolongation of (8, 15)-Distribution of Type ₄ by Singular Curves |
| title_sort | prolongation of (8, 15)-distribution of type ₄ by singular curves |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/214092 |
| work_keys_str_mv | AT ishikawagoo prolongationof815distributionoftype4bysingularcurves AT machidayoshinori prolongationof815distributionoftype4bysingularcurves |