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The geometry of a bi-Lagrangian manifold. (English) Zbl 1101.53047

In this survey the authors study bi-Lagrangian manifolds. Bi-Lagrangian manifolds are symplectic manifolds with two transversal Lagrangian foliations. The authors also consider the case when the two transversal Lagrangian distributions are non-integrable. They show that many different geometric structures can be attached to these manifolds and they analyze the associated connections. They introduce the problem of the intersection of the two leaves of the foliations.

MSC:

53D05 Symplectic manifolds (general theory)
53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.)
53C05 Connections (general theory)
53C12 Foliations (differential geometric aspects)
57R30 Foliations in differential topology; geometric theory
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