The geometry of a bi-Lagrangian manifold
Symplectic Geometry
2015-12-14 v1 Differential Geometry
Abstract
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.
Cite
@article{arxiv.math/0403512,
title = {The geometry of a bi-Lagrangian manifold},
author = {Fernando Etayo and Rafael Santamaría and Ujué R. Trías},
journal= {arXiv preprint arXiv:math/0403512},
year = {2015}
}
Comments
30 pages