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Let be a holomorphic foliation with reduced singularities on a complex surface M and a real analytic codimension one foliation on M whose leaves contain the ones of . We show that a Levi flat group of diffeomorphisms of is resoluble and holomorphically conjugate to his normal form. We deduce, in one hand, that each singularity of  is conjugate to his normal form. In the other hand at each singularity m of , where is not defined, up a conjugacy, by the one form ω=xdy+ydx, one of the local invariant curves of , with non obvious holonomy, is contained in the set of singularities of . Moreover if M is a compact Stein variety we show, under some generic conditions, that has a 1-Liouvillian first integrating factor.  相似文献   

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On prouve que la caractéristique d'Euler d'un feuilletage mesuré est nulle si et seulement si celui-ci admet un champ tangent transversalement mesurable dont l'ensemble de singularités est de mesure arbitrairement petite. Si le feuilletage est moyennable, alors on peut construire un tel champ sans singularités. Si les feuilles sont de dimension deux, l'annulation de la caractéristique d'Euler implique la moyennabilité ; plus encore, elle équivaut à l'existence d'une action mesurable de R2 sur la variété ambiant qui est continue et localement libre sur chaque feuille.  相似文献   

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We study the dynamics of automorphisms of complex projective surfaces. Letbe such an automorphism whose topological entropy is not zero. We construct a probability measure associated toand the complex structure. This measure is -invariant, ergodic and has maximal entropy. This is the unique measure satisfying these properties and periodic points are equidistributed with respect to this measure.  相似文献   

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Let (M.g) be a closed orientable surface, equipped with a Finsler metric. The metric induces a norm on the real homology of M, called stable norm. We show this norm is not strictly convex.  相似文献   

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Resumé On démontre qu'une 3-variété hyperbolique compacte n'admet pas de feuilletageC 0, dont les feuilles sont géodésiques.
Summary We prove that a compact hyperbolic 3-manifold does not possess aC 0 foliation, with geodesic leaves.


Oblatum II-1993  相似文献   

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Let F be a transversely holomorphic codimension n foliation on a compact orientable manifold M and E a foliated holomorphic vector bundle on M. We prove that the cohomology of M with coefficients in the sheaf of E-valued holomorphic base-like differential forms satisfies Serre duality. Some computations are given. In case n=1 we show that the base-like cohomology H*(M/F,) is finite dimensional.  相似文献   

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