Smooth foliations on homogeneous compact Kähler manifolds

— In this paper we prove that a regular foliation on a complex weak Fano manifold is algebraically integrable..

In [9] good convergence prop- erties were obtained (in the setting of domains in C n ) under the assumption that all the Monge-Amp`ere measures are dominated by a fixed

Then (up to replacing X by a finite étale cover) the manifold G is either projective or does not contain any positive-dimensional compact proper

The aim of this paper is to prove that the set of the quotient Ox-modules of ©x which satisfy conditions (i) and (ii) of definition 2 is an analytic subspace Jf of an open set of H

Section 4 applies the results to the general symplectic case and with Section 5 shows that the homo- geneous manifold M can be split —as a homogeneous symplectic space— into a

— If S is compact (i.e., if N = G/K is compact mth finite fundamental group), there exists a connected, open, dense, ^f-saturated submani' fold V of M which fibers over a

Moreover these conditions imply that some neighbourhood of L consists of a union of compact leaves and that in this neighbourhood the equivalent conditions of Theorem 4.1 are

For example, the existence of a codimension-one foliation follows from the existence of a spinnable structure having an odd dimensional sphere a.s axis (see Theorem 5).. Thus