0000000000617563
AUTHOR
R. Langevin
Feuilletages deCP(n) : de l’holonomie hyperbolique pour les minimaux exceptionnels
Let ℱ be a holomorphic foliation ofCP(n). If ℱ has a leaf L, the closure L of which is disjoint from the singular set of the foliation, we prove that there exists a loop in a leaf contained in L with contracting hyperbolic holonomy.
Three viewpoints on the integral geometry of foliations
We deal with three different problems of the multidimensional integral geometry of foliations. First, we establish asymptotic formulas for integrals of powers of curvature of foliations obtained by intersecting a foliation by affine planes. Then we prove an integral formula for surfaces of contact of an affine hyperplane with a foliation. Finally, we obtain a conformally invariant integral-geometric formula for a foliation in three-dimensional space.