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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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2025 |
| ISSN: | 1815-0659 |
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Інститут математики НАН України
2025
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| Online Zugang: | 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 |
| Zitieren: | Prolongation of (8, 15)-Distribution of Type ₄ by Singular Curves. Goo Ishikawa and Yoshinori Machida. SIGMA 21 (2025), 076, 20 pages |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Zusammenfassung: | 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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| ISSN: | 1815-0659 |