Courbes entières dans les surfaces algébriques complexes
On the topological equivalence between Anosov flows on the three-manifolds.
Instability of equilibria in dimension three
In this paper we show that if is an analytic vector field on having an isolated singular point at 0, then there exists a trajectory of which converges to 0 in the past or in the future. The proof is based on certain results concerning desingularizaton of vector fields in dimension three and on index-type arguments .
Foliations on the complex projective plane with many parabolic leaves
We prove that a foliation on with hyperbolic singularities and with “many" parabolic leaves (i.e. leaves without Green functions) is in fact a linear foliation. This is done in two steps: first we prove that there exists an algebraic leaf, using the technique of harmonic measures, then we show that the holonomy of this leaf is linearizable, from which the result follows easily.
Singular Levi-flat hypersurfaces and codimension one foliations
We study Levi-flat real analytic hypersurfaces with singularities. We prove that the Levi foliation on the regular part of the hypersurface can be holomorphically extended, in a suitable sense, to neighbourhoods of singular points.
Feuilletages holomorphes sur les surfaces complexes compactes
Some remarks on indices of holomorphic vector fields.
One can associate several residue-type indices to a singular point of a two-dimensional holomorphic vector field. Some of these indices depend also on the choice of a separatrix at the singular point. We establish some relations between them, especially when the singular point is a generalized curve and the separatrix is the maximal one. These local results have global consequences, for example concerning the construction of logarithmic forms defining a given holomorphic foliation.
Minimal models of foliated algebraic surfaces
Codimension one foliations on complex tori
We prove a structure theorem for codimension one singular foliations on complex tori, from which we deduce some dynamical consequences.
Un complément à l’article de Dloussky sur le colmatage des surfaces holomorphes
Nous étudions les surfaces complexes compactes qui sont des dégénérations de surfaces de Hopf éclatées. Nous démontrons que si une telle surface contient une hypersurface réelle globale strictement pseudoconvexe, alors est une surface de Kato. Ceci permet d’améliorer un résultat de Dloussky, paru dans ce même journal en 1993.
On the discrete Godbillon-Vey invariant and Dehn surgery on geodesic flows
Holomorphic foliations in certain holomorphically convex domains of
Bounding the degree of solutions to Pfaff equations
We study hypersurfaces of complex projective manifolds which are invariant by a foliation, or more generally which are solutions to a Pfaff equation. We bound their degree using classical results on logarithmic forms.
On the automorphism group of a complex sphere.
Kähler manifolds with split tangent bundle
This paper is concerned with compact Kähler manifolds whose tangent bundle splits as a sum of subbundles. In particular, it is shown that if the tangent bundle is a sum of line bundles, then the manifold is uniformised by a product of curves. The methods are taken from the theory of foliations of (co)dimension 1.
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