The geometry of a bi-Lagrangian manifold

Details The geometry of a bi-Lagrangian manifold The geometry of a bi-Lagrangian manifold

2004-03-30

arxiv.org/abs/math/0403512v1

Mathematics

Symplectic Geometry

30 pages

Scientific paper

This is a survey on bi-Lagrangian manifolds, which are symplectic manifolds endowed with two transversal Lagrangian foliations. We also study the non-integrable case (i.e., a symplectic manifold endowed with two transversal Lagrangian distributions). We show that many different geometric structures can be attached to these manifolds and we carefully analyse the associated connections. Moreover, we introduce the problem of the intersection of two leaves, one of each foliation, through a point and show a lot of significative examples.

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