Session S39 - Differential Equations and Geometric Structures

Wednesday, July 14, 13:00 ~ 13:50 UTC-3

Foliated affine and projective structures

Adolfo Guillot

UNAM, Mexico   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

We discuss the existence of foliated affine and projective structures along the leaves of a holomorphic foliation by curves (varying holomorphically in the transverse direction). We will see that there are many foliations that admit them. We will give an index formula that allows to show that there are also many foliations do not admit these structures. For instance, a non-singular foliation of general type on a manifold of even dimension does not admit a foliated projective structure.

Joint work with Bertrand Deroin.

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