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Sur la géométrie des sous-fibres et des feuilletages lagrangiens. (French) Zbl 0491.58015


MSC:

37J99 Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems
57R20 Characteristic classes and numbers in differential topology
70H99 Hamiltonian and Lagrangian mechanics
53C12 Foliations (differential geometric aspects)
53C40 Global submanifolds
57R30 Foliations in differential topology; geometric theory
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References:

[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 35 #334 | Zbl 0149.21704 · Zbl 0149.21704
[3] R. BOTT , On a Topological Obstruction to Integrability (Proc. Symp. in Pure Math. A.M.S., vol. 16, 1970 , p. 127-131). MR 42 #1155 | Zbl 0206.50501 · Zbl 0206.50501
[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^\circ 2, 1979 , p. 25-78; (c) Variations sur la classe de Maslov-Arnold [Journées P. de Fermat, Toulouse, 1981 (à paraître)]. MR 58 #24402 · Zbl 0315.53023
[5] J. HAYDEN et E. C., ZEEMAN , A Lagrangian Klein Bottle (Math. Proc. Cam. Phil. Soc., 1980 , p. 89-193). MR 82c:58009 | Zbl 0465.58009 · Zbl 0465.58009
[6] KOBAYASHI et K. NOMIZU , Foundations of Differential Geometry (Interscience, 1969 ). MR 38 #6501 · Zbl 0175.48504
[7] J. LERAY , Analyse lagrangienne et Mécanique quantique , Collège de France, 1977 . Numdam | MR 58 #18617
[8] P. LIBERMANN , Sur le problème d’équivalence de certaines structures infinitésimales (Thèse, Strasbourg, 1953 ). Article
[9] A. LICHNEROWICZ , Théorie Globale des Connexions et de groupes d’holonomie , Cremonese, 1955 . Zbl 0116.39101 · Zbl 0116.39101
[10] J. M. MORVAN , Classe de Maslov d’une immersion lagrangienne [C. R. Acad. Sc., Paris (à paraître)]. · Zbl 0466.53030
[11] A. WEINSTEIN , Lecture on Symplectic Manifolds, Conference board of mathematical science (Regional Conference Series in Mathematics n^\circ 29, A.M.S., 1977 ). MR 57 #4244 | Zbl 0406.53031 · Zbl 0406.53031
[12] J. A. WOLF , Spaces of Constant Curvature , MacGraw Hill, 1967 . MR 36 #829 | Zbl 0162.53304 · Zbl 0162.53304
[13] K. YANO et M. KON , Antiinvariant Submanifolds (Lecture Notes in Pure and Appl. Math., vol. 21, Marcel Dekker, 1976 ). MR 54 #13799 | Zbl 0349.53055 · Zbl 0349.53055
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