Teoria Geomètrica de Foliacions

This project deals with the study of geometric properties of foliations on manifolds and it can be considered as continuation of the above DGICYT projects of our group. From the geometrical study of the holomorphic dynamical systems we have developed a general method to construct non algebraic compact complex manifolds. By considering the action of some Lie groups different from C, for instance the complex affine group or PSL (2,C), we will try hewre to generalize the method of construction given above. The study of foliated harmonic maps will be pursuited. In order to study the existence of such maps when the target manifold has trivial second homotopy group we must develope a suitable equivariant Morse theory on Banach manifolds. We are also interested in the continuation of our previous work on sympletic linerization of Lagrangian foliations, that is the study of the invariants which determine the germ of the foliation in the neighborhood of a compact leaf. The central point is to use the natural affine structure of this leaf.