Real and complex transversely symplectic Anosov flows of dimension five
Séminaire de théorie spectrale et géométrie, Volume 23 (2004), pp. 105-114

Nous présentons plusieurs résultats de rigidité concernant les flots d’Anosov admettant transversalement des structures symplectiques réelles ou complexes de dimension 5.

We present several rigidity results about five-dimensional real or complex transversely symplectic Anosov flows.

DOI: 10.5802/tsg.232
Classification: 37D40, 53C25 
Yong Fang. Real and complex transversely symplectic Anosov flows of dimension five. Séminaire de théorie spectrale et géométrie, Volume 23 (2004), pp. 105-114. doi: 10.5802/tsg.232
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[B] M. Brunella, On transversely holomorphic flows I, Invent. Math., 126 (1996), 265–279. | Zbl | MR

[BFL] Y. Benoist, P. Foulon and F. Labourie, Flots d’Anosov à distributions de Liapounov différentiables. I, Ann. Inst. Henri Poincaré, 53 (1990), 395–412. | Zbl | Numdam

[BFL1] Y. Benoist, P. Foulon and F. Labourie, Flots d’Anosov à distributions stable et instable différentiables, J. Amer. Math. Soc., 5 (1992), 33–74. | Zbl

[CIPP] G. Contreras, R. Iturriaga, G. P. Paternain and M. Paternain, Lagrangian graphs, minimizing measures and Mané’s critical values, GAFA, 8 (1998) 788–809. | Zbl

[D] S. Dumitrescu, Métriques riemanniennes holomorphesen petite dimension, Ann. Inst. Fourier, 51, 6 (2001), 1663–1690. | Zbl | MR | Numdam

[F] Y. Fang, Structures géométriques rigides et systèmes dynamiques hyperboliques, ph.D. thesis, University of Paris-Sud. Web address: http://tel.archives-ouvertes.fr/tel-00008734/fr/

[F1] Y. Fang, Geometric Anosov flows of dimension 5 with smooth distributions, to appear in Journal of the Institute of Mathematics of Jussieu. Web address: http://hal.ccsd.cnrs.fr/ccsd-00004411 | Zbl | MR

[F2] Y. Fang, Smooth rigidity of uniformly quasiconformal Anosov flows, Ergod. Th. and Dynam. Sys, 24 (2004), 1937–1959. | Zbl | MR

[F3] Y. Fang, On orbit equivalence of quasiconformal Anosov flows, soumitted. Web address: http://hal.ccsd.cnrs.fr/ccsd-00004412

[FK] R. Feres and A. Katok, invariant tensor fields of dynamical systems with pinched Lyapunov exponents and rigidity of geodesic flows, Ergod. Th. and Dynam. Sys., 9 (1989), 427–432. | Zbl | MR

[G] É. Ghys, Flots d’Anosov dont les feuilletages stables sont différentiables, Ann. Scient. Éc. Norm. Sup. (4), 20 (1987), 251–270. | Zbl | Numdam

[G1] É. Ghys, Holomorphic Anosov flows, Invent. math., 119 (1995), 585–614. | Zbl | MR

[G2] É. Ghys, On transversely holomorphic flows II, Invent. Math., 126 (1996) 281–286. | Zbl | MR

[HK] B. Hasselblatt and A. Katok, Introduction to the modern theory of dynamical systems, Encyclopedia of Mathematics and its Applications, vol 54, 1995. | Zbl | MR

[HuK] S. Hurder and A. Katok, Differentiability, rigidity and Godbillon-Vey classes for Anosov flows, Pub. I.H.É.S., 72 (1990), 5–61. | Zbl | MR | Numdam

[IKO] M. Inoue, S. Kobayashi and T. Ochiai, Holomorphic affine connections on compact complex surfaces, J. Fac. Sci. Univ. Tokyo, 27(2) (1980), 247-264. | Zbl | MR

[K] M. Kanai, Geodesic flows of negatively curved manifolds with smooth stable and instable foliations, Ergod. Th. and Dynam. Sys., 8 (1988), 215–240. | Zbl | MR

[S] V. Sadovskaya, On uniformly quasiconformal Anosov systems, nto appear in Math. Res. Lett. | Zbl | MR

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