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.
Let be a smooth foliation with complex leaves and let be the sheaf of germs of smooth functions, holomorphic along the leaves. We study the ringed space . In particular we concentrate on the following two themes: function theory for the algebra and cohomology with values in .
We obtain a classification of codimension one holomorphic foliations on with degenerate Gauss maps.
Si illustrano alcuni sviluppi della teoria delle foliazioni di Monge-Ampère e delle sue applicazioni alla classificazione delle varietà complesse non compatte.
Soit un morphisme propre fini et surjectif entre deux variétés analytiques complexes. Nous donnons une caractérisation des fonctions (continues) sur qui sont de la forme où est une fonction sur . Pour cela nous introduisons la notion de fonction de type trace sur une variété analytique complexe. Ces fonctions sont analytiques réelles en dehors d’une hypersurface complexe et admettent des singularités très simples aux points de cette hypersurface.
We define the notion of CR equivalence for Levi-flat foliations and compare in a local setting these foliations to their linear parts. We study also the situation where the foliation has a first integral ; a condition is given so that this integral is the real part of a holomorphic function.