Czechoslovak Mathematical Journal, first online, pp. 1-20


Stability of certain Engel-like distributions

Aritra Bhowmick

Received March 2, 2020.   Published online December 18, 2020.

Abstract:  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.
Keywords:  Engel structure; Cartan prolongation; global stability; nonholonomic distribution; normal form
Classification MSC:  58A30, 58A15, 58A17
DOI:  10.21136/CMJ.2020.0093-20

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References:
[1] J. Adachi: 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] J. Adachi: Global stability of special multi-flags. Isr. J. Math. 179 (2010), 29-56. DOI 10.1007/s11856-010-0072-3  | MR 2735034 | Zbl 1222.58003
[3] R. L. Bryant, S. S. Chern, R. B. Gardner, H. L. Goldschmidt, P. A. Griffiths: 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] E. A. Coddington, N. Levinson: Theory of Ordinary Differential Equations. McGraw- Hill, New York (1955). MR 0069338 | Zbl 0064.33002
[5] A. Golubev: 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] J. W. Milnor, J. D. Stasheff: Characteristic Classes. Annals of Mathematics Studies 76. Princeton University Press, Princeton (1974). DOI 10.1515/9781400881826 | MR 0440554 | Zbl 0298.57008
[7] R. Montgomery: 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] R. Montgomery: 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] R. Montgomery, M. Zhitomirskii: 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] P. Mormul: 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

Affiliations:   Aritra Bhowmick, Statistics and Mathematics Unit, Indian Statistical Institute, 203, B.T. Road, Kolkata 700108, India, e-mail: avowmix@gmail.com


 
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