Previous |  Up |  Next

Article

Keywords:
Engel structure; Cartan prolongation; global stability; nonholonomic distribution; normal form
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.
References:
[1] Adachi, J.: Global stability of distributions of higher corank of derived length one. Int. Math. Res. Not. 49 (2003), 2621-2638. DOI 10.1155/S1073792803130735 | MR 2012520 | Zbl 1044.58007
[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}. DOI 10.1007/s11856-010-0072-3 | MR 2735034 | Zbl 1222.58003
[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). DOI 10.1007/978-1-4613-9714-4 | MR 1083148 | Zbl 0726.58002
[4] Coddington, E. A., Levinson, N.: Theory of Ordinary Differential Equations. McGraw- Hill, New York (1955). MR 0069338 | Zbl 0064.33002
[5] Golubev, A.: On the global stability of maximally nonholonomic two-plane fields in four dimensions. Int. Math. Res. Not. 1997 (1997), 523-529. DOI 10.1155/S1073792897000342 | MR 1448335 | Zbl 0893.58007
[6] Milnor, J. W., Stasheff, J. D.: Characteristic Classes. Annals of Mathematics Studies 76. Princeton University Press, Princeton (1974). DOI 10.1515/9781400881826 | MR 0440554 | Zbl 0298.57008
[7] Montgomery, R.: Generic distributions and Lie algebras of vector fields. J. Differ. Equations 103 (1993), 387-393. DOI 10.1006/jdeq.1993.1056 | MR 1221912 | Zbl 0782.58008
[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. DOI 10.1090/trans2/196/07 | MR 1736216 | Zbl 0961.53043
[9] Montgomery, R., Zhitomirskii, M.: Geometric approach to Goursat flags. Ann. Inst. Henri Poincaré, Anal. Non Linéaire 18 (2001), 459-493. DOI 10.1016/S0294-1449(01)00076-2 | MR 1841129 | Zbl 1013.58004
[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. DOI 10.4064/bc65-0-12 | MR 2104345 | Zbl 1056.58002
Partner of
EuDML logo