The cohomology of various sheaves associated with a Lagrangian foliation is discussed. Obstructions for the foliation either to behave like in the case of a cotangent bundle or to have an affine transversal distribution are found in this cohomology. Furthermore, one proves a formula for all the symplectic structures of a cotangent bundle such that the fibers constitute a Lagrangian foliation.
ASJC Scopus subject areas
- Mathematics (all)