Sur la géométrie des sous-fibrés et des feuilletages lagrangiens
Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 14 (1981) no. 4, pp. 465-480.
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Dazord, Pierre. Sur la géométrie des sous-fibrés et des feuilletages lagrangiens. Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 14 (1981) no. 4, pp. 465-480. doi : 10.24033/asens.1416. https://www.numdam.org/articles/10.24033/asens.1416/

[1] V. I. Arnold, Une classe caractéristique intervenant dans les conditions de quantification (en français dans Maslov). Théorie des perturbations et méthodes asymptotiques, Dunod-Gauthier-Villars, Paris, 1972, p. 341-361.

[2] V. I. Arnold et A. Avez, Problèmes ergodiques de la mécanique classique, Gauthier-Villars, Paris, 1967. | MR | Zbl

[3] R. Bott, On a Topological Obstruction to Integrability (Proc. Symp. in Pure Math. A.M.S., vol. 16, 1970, p. 127-131). | MR | Zbl

[4] P. Dazord, (a) Une interprétation géométrique de la classe de Maslov (J. Math. Pures et Appl., vol. 56, 1977, p. 231-250; (b) Invariants homotopiques attachés aux fibrés symplectiques (Ann. Inst. Fourier, Grenoble, vol. 29, n° 2, 1979, p. 25-78; (c) Variations sur la classe de Maslov-Arnold [Journées P. de Fermat, Toulouse, 1981 (à paraître)]. | MR

[5] J. Hayden et E. C., Zeeman, A Lagrangian Klein Bottle (Math. Proc. Cam. Phil. Soc., 1980, p. 89-193). | MR | Zbl

[6] Kobayashi et K. Nomizu, Foundations of Differential Geometry (Interscience, 1969). | MR

[7] J. Leray, Analyse lagrangienne et Mécanique quantique, Collège de France, 1977. | Numdam | MR

[8] P. Libermann, Sur le problème d'équivalence de certaines structures infinitésimales (Thèse, Strasbourg, 1953).

[9] A. Lichnerowicz, Théorie Globale des Connexions et de groupes d'holonomie, Cremonese, 1955. | Zbl

[10] J. M. Morvan, Classe de Maslov d'une immersion lagrangienne [C. R. Acad. Sc., Paris (à paraître)].

[11] A. Weinstein, Lecture on Symplectic Manifolds, Conference board of mathematical science (Regional Conference Series in Mathematics n° 29, A.M.S., 1977). | MR | Zbl

[12] J. A. Wolf, Spaces of Constant Curvature, MacGraw Hill, 1967. | MR | Zbl

[13] K. Yano et M. Kon, Antiinvariant Submanifolds (Lecture Notes in Pure and Appl. Math., vol. 21, Marcel Dekker, 1976). | MR | Zbl

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  • Kajigaya, Toru On the Hamiltonian Minimality of Normal Bundles, Real and Complex Submanifolds, Volume 106 (2014), p. 485 | DOI:10.1007/978-4-431-55215-4_43
  • Schäfer, Lars On the HSL-flow, Calculus of Variations and Partial Differential Equations, Volume 46 (2013) no. 1-2, p. 311 | DOI:10.1007/s00526-011-0483-y
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  • Hunter, Richard; McIntosh, Ian The classification of Hamiltonian stationary Lagrangian tori in CP2 by their spectral data, Manuscripta Mathematica, Volume 135 (2011) no. 3-4, p. 437 | DOI:10.1007/s00229-010-0425-6
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  • DE BARTOLOMEIS, PAOLO; TOMASSINI, ADRIANO SOME RESULTS ON GENERALIZED CALABI–YAU MANIFOLDS, International Journal of Geometric Methods in Modern Physics, Volume 03 (2006) no. 05n06, p. 1273 | DOI:10.1142/s0219887806001508
  • Hijazi, O.; Montiel, S.; Urbano, F. Spinc geometry of Kähler manifolds and the Hodge Laplacian on minimal Lagrangian submanifolds, Mathematische Zeitschrift, Volume 253 (2006) no. 4, p. 821 | DOI:10.1007/s00209-006-0936-8
  • ONO, Hajime Integral formula of Maslov index and its applications, Japanese journal of mathematics. New series, Volume 30 (2004) no. 2, p. 413 | DOI:10.4099/math1924.30.413
  • Amarzaya, Amartuvshin; Ohnita, Yoshihiro Hamiltonian stability of certain minimal Lagrangian submanifolds in complex projective spaces, Tohoku Mathematical Journal, Volume 55 (2003) no. 4 | DOI:10.2748/tmj/1113247132
  • Karasev, Mikhail; Vorobjev, Yuri Integral Representations over Isotropic Submanifolds and Equations of Zero Curvature, Advances in Mathematics, Volume 135 (1998) no. 2, p. 220 | DOI:10.1006/aima.1997.1703
  • Currás-Bosch, Carlos; Molino, Pierre Holonomie, suspensions et classifications pour les feuilletages lagrangiens, Comptes Rendus de l'Académie des Sciences - Series I - Mathematics, Volume 326 (1998) no. 11, p. 1317 | DOI:10.1016/s0764-4442(98)80186-9
  • Currás-Bosch, Carlos; Molino, Pierre Un exemple de classification de germes de feuilletages Lagrangiens au voisinage d'une feuille compacte, Indagationes Mathematicae, Volume 9 (1998) no. 2, p. 197 | DOI:10.1016/s0019-3577(98)80018-9
  • Wolfson, Jon G. Minimal Lagrangian diffeomorphisms and the Monge-Ampère equation, Journal of Differential Geometry, Volume 46 (1997) no. 2 | DOI:10.4310/jdg/1214459935
  • Karasev, M. V.; Vorobjev, Yu. M. Symplectic curvature and the arnold form over and isotropic submanifold, Journal of Mathematical Sciences, Volume 82 (1996) no. 6, p. 3789 | DOI:10.1007/bf02362638
  • Oh, Yong-Geun Mean curvature vector and symplectic topology of Lagrangian submanifolds in Einstein-Kähler manifolds, Mathematische Zeitschrift, Volume 216 (1994) no. 1, p. 471 | DOI:10.1007/bf02572335
  • Karasev, Michael; Vorobjev, Yurij Linear Connections for Hamiltonian Dynamics over Isotropic Submanifold, Seminar on Dynamical Systems (1994), p. 235 | DOI:10.1007/978-3-0348-7515-8_18
  • Dazord, P.; Patissier, G. La Première Classe de Chern Comme Obstruction à la Quantification Asymptotique, Symplectic Geometry, Groupoids, and Integrable Systems, Volume 20 (1991), p. 73 | DOI:10.1007/978-1-4613-9719-9_5
  • Dazord, Pierre; Delzant, Thomas Le Probleme General des Variables Actions-Angles, Journal of Differential Geometry, Volume 26 (1987) no. 2 | DOI:10.4310/jdg/1214441368
  • Vaisman, I. The Maslov class of some Legendre submanifolds, Journal of Geometry and Physics, Volume 3 (1986) no. 3, p. 289 | DOI:10.1016/0393-0440(86)90010-0
  • Dazord, P. Erratum: ”Sur la géométrie des sous-fibrés et des feuilletages lagrangiens”, Annales Scientifiques de l'École Normale Supérieure. Quatrième Série, Volume 18 (1985), p. 685 | DOI:10.24033/asens.1501 | Zbl:0596.58020
  • Grifone, J.; Hassan, E. Connexions singulieres et classe de Maslov, Differential Geometry, Volume 1045 (1984), p. 71 | DOI:10.1007/bfb0072167
  • Dazord, P. Variations sur la classe de Maslov-Arnold, Symplectic geometry, Res. Notes Math. 80, 38-44, 1983 | Zbl:0516.53041

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