Abstract
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.
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This paper has been written while the author was a visiting professor at the Universities of Montpellier and Strasbourg (France). He wants to acknowledge here his gratitude to these host institutions, and, particularly, to Pierre Molino, Claude Godbillon and Daniel Bernard.
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Vaisman, I. d f-cohomology of Lagrangian foliations. Monatshefte für Mathematik 106, 221–244 (1988). https://doi.org/10.1007/BF01318683
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DOI: https://doi.org/10.1007/BF01318683