Stability of certain Engel-like distributions
Czechoslovak Mathematical Journal, Tome 71 (2021) no. 3, pp. 765-784
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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.
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.
DOI : 10.21136/CMJ.2020.0093-20
Classification : 58A15, 58A17, 58A30
Keywords: Engel structure; Cartan prolongation; global stability; nonholonomic distribution; normal form
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     title = {Stability of certain {Engel-like} distributions},
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Bhowmick, Aritra. Stability of certain Engel-like distributions. Czechoslovak Mathematical Journal, Tome 71 (2021) no. 3, pp. 765-784. doi: 10.21136/CMJ.2020.0093-20

[1] Adachi, J.: Global stability of distributions of higher corank of derived length one. Int. Math. Res. Not. 49 (2003), 2621-2638. | DOI | MR | JFM

[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 | MR | JFM

[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 | MR | JFM

[4] Coddington, E. A., Levinson, N.: Theory of Ordinary Differential Equations. McGraw- Hill, New York (1955). | MR | JFM

[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 | MR | JFM

[6] Milnor, J. W., Stasheff, J. D.: Characteristic Classes. Annals of Mathematics Studies 76. Princeton University Press, Princeton (1974). | DOI | MR | JFM

[7] Montgomery, R.: Generic distributions and Lie algebras of vector fields. J. Differ. Equations 103 (1993), 387-393. | DOI | MR | JFM

[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 | MR | JFM

[9] Montgomery, R., Zhitomirskii, M.: Geometric approach to Goursat flags. Ann. Inst. Henri Poincaré, Anal. Non Linéaire 18 (2001), 459-493. | DOI | MR | JFM

[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 | MR | JFM

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