| Title:
             | 
Stability of certain Engel-like distributions (English) | 
| Author:
             | 
Bhowmick, Aritra | 
| Language:
             | 
English | 
| Journal:
             | 
Czechoslovak Mathematical Journal | 
| ISSN:
             | 
0011-4642 (print) | 
| ISSN:
             | 
1572-9141 (online) | 
| Volume:
             | 
71 | 
| Issue:
             | 
3 | 
| Year:
             | 
2021 | 
| Pages:
             | 
765-784 | 
| Summary lang:
             | 
English | 
| . | 
| Category:
             | 
math | 
| . | 
| Summary:
             | 
We introduce a higher dimensional analogue of the Engel structure, motivated by the Cartan prolongation of contact manifolds. We study the stability of such structure, generalizing the Gray-type stability results for Engel manifolds. We also derive local normal forms defining such a distribution. (English) | 
| Keyword:
             | 
Engel structure | 
| Keyword:
             | 
Cartan prolongation | 
| Keyword:
             | 
global stability | 
| Keyword:
             | 
nonholonomic distribution | 
| Keyword:
             | 
normal form | 
| MSC:
             | 
58A15 | 
| MSC:
             | 
58A17 | 
| MSC:
             | 
58A30 | 
| idZBL:
             | 
07396196 | 
| idMR:
             | 
MR4295244 | 
| DOI:
             | 
10.21136/CMJ.2020.0093-20 | 
| . | 
| Date available:
             | 
2021-08-02T08:06:00Z | 
| Last updated:
             | 
2023-10-02 | 
| Stable URL:
             | 
http://hdl.handle.net/10338.dmlcz/149055 | 
| . | 
| Reference:
             | 
[1] Adachi, J.: Global stability of distributions of higher corank of derived length one.Int. Math. Res. Not. 49 (2003), 2621-2638. Zbl 1044.58007, MR 2012520, 10.1155/S1073792803130735 | 
| Reference:
             | 
[2] Adachi, J.: Global stability of special multi-flags.Isr. J. Math. 179 (2010), 29-56 \99999DOI99999 10.1007/s11856-010-0072-3 \hyphenation{Dif-fer-en-tial}. Zbl 1222.58003, MR 2735034, 10.1007/s11856-010-0072-3 | 
| Reference:
             | 
[3] Bryant, 	R. L., Chern, S. S., Gardner, R. B., Goldschmidt, H. L., Griffiths, P. A.: Exterior Differential Systems.Mathematical Sciences Research Institute Publications 18. Springer, New York (1991). Zbl 0726.58002, MR 1083148, 10.1007/978-1-4613-9714-4 | 
| Reference:
             | 
[4] Coddington, E. A., Levinson, N.: Theory of Ordinary Differential Equations.McGraw- Hill, New York (1955). Zbl 0064.33002, MR 0069338 | 
| Reference:
             | 
[5] Golubev, 	A.: On the global stability of maximally nonholonomic two-plane fields in four dimensions.Int. Math. Res. Not. 1997 (1997),	523-529. Zbl 0893.58007, MR 1448335, 10.1155/S1073792897000342 | 
| Reference:
             | 
[6] Milnor, J. W., Stasheff, J. D.: Characteristic Classes.Annals of Mathematics Studies 76. Princeton University Press, Princeton (1974). Zbl 0298.57008, MR 0440554, 10.1515/9781400881826 | 
| Reference:
             | 
[7] Montgomery, 	R.: Generic distributions and Lie algebras of vector fields.J. Differ. Equations 103 (1993), 387-393. Zbl 0782.58008, MR 1221912, 10.1006/jdeq.1993.1056 | 
| Reference:
             | 
[8] Montgomery, R.: Engel deformations and contact structures.Northern California Symplectic Geometry Seminar 	American Mathematical Society Translations: Series 2, Volume 196. American Mathematical Society, Providence (1999), 103-117. Zbl 0961.53043, MR 1736216, 10.1090/trans2/196/07 | 
| Reference:
             | 
[9] Montgomery, 	R., Zhitomirskii, M.: Geometric approach to Goursat flags.Ann. Inst. Henri Poincaré, Anal. Non Linéaire 18 (2001),	459-493. Zbl 1013.58004, MR 1841129, 10.1016/S0294-1449(01)00076-2 | 
| Reference:
             | 
[10] Mormul, P.: Multi-dimensional Cartan prolongation and special $k$-flags.Geometric Singularity Theory Banach Center Publications 65. Polish Academy of Sciences, Institute of Mathematics, Warsaw (2004),	157-178. Zbl 1056.58002, MR 2104345, 10.4064/bc65-0-12 | 
| . |