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Open Engel manifolds admitting compact characteristic leaves

Published online by Cambridge University Press:  17 April 2009

Takashi Inaba
Takashi Inaba
Affiliation:
Division of Mathematical Sciences and Physics, Graduate School of Science and Technology, Chiba University, 1-33 Yayoicho, Inage-ku, Chiba 263-8522, Japan, e-mail: [email protected]
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Abstract

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We give an example of an Engel structure on the 4-dimensional Euclidean space which admits a compact characteristic leaf. We also show that every Engel structure on an open 4-manifold can be modified so that the resulting structure has a compact characteristic leaf.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 68 , Issue 2 , October 2003 , pp. 213 - 219
Copyright
Copyright © Australian Mathematical Society 2003

References

[1]Bryant, R.L., Chern, S.S., Gardner, R.B., Goldschmidt, H.L. and Griffiths, P.A., Exterior differential systems, Math. Sci. Res. Inst. Publ. 18 (Springer Verlag, New York, 1991).CrossRefGoogle Scholar
[2]Bryant, R.L. and Hsu, L., ‘Rigidity of integral curves of rank 2 distributions’, Invent. Math. 114 (1993), 435–461.CrossRefGoogle Scholar
[3]Gershkovich, V., ‘Engel structures on four dimensional manifolds’, (preprint, Univ. of Melbourne, 1993).Google Scholar
[4]Gershkovich, V., ‘Exotic Engel structures on R4’, Russian J. Math. Phys. 3 (1995), 207–226.Google Scholar
[5]Golubev, A., ‘On the stability of maximally nonholonomic two-plane fields in four dimensions’, Internat. Math. Res. Notices 11 (1997), 523–529.CrossRefGoogle Scholar
[6]Lutz, R., ‘Structures de contact sur les fibres principaux en circles de dimension trios’, Ann. Inst. Fourier (Grenoble) 27 (1977), 1–15.CrossRefGoogle Scholar
[7]Milnor, J., Morse theory, Ann. of Math. Studies 51 (Princeton Univ. Press, Princeton, N. J., 1963).CrossRefGoogle Scholar
[8]Montgomery, R., ‘Engel deformations and contact structures’, in Northern California symplectic geometry seminar, Amer. Math. Soc. Trans. Ser. 2 196 (Amer. Math. Soc., Providence, R.I., 1999), pp. 103–117.Google Scholar
[9]Montgomery, R. and Zhitomirskii, M., ‘Geometric approach to Goursat flags’, Ann. Inst. H. Poincaré Anal. Non Linéaire 18 (2001), 459–493.CrossRefGoogle Scholar