The canonical connection of a bi-Lagrangian manifold (Q2716219)

The authors study geometric properties of a symplectic manifold endowed with a Lagrangian distribution and with two transversal Lagrangian distributions. The main results are the following. NEWLINENEWLINENEWLINETheorem 1. A symplectic manifold endowed with a Lagrangian distribution admits infinitely many Lagrangian distributions. NEWLINENEWLINENEWLINETheorem 2. If a Kähler manifold admits a Lagrangian foliation \(\mathcal F\) which is preserved by the Levi-Civita connection \(\nabla\), then its orthogonal distribution defines a foliation \(\mathcal F^\perp\) and the canonical connection of the bi-Lagrangian structure defined by \(\mathcal F\) and \(\mathcal F^\perp\) is \(\nabla\). NEWLINENEWLINENEWLINETheorem 3. A bi-Lagrangian manifold is endowed with a canonical semi-Riemannian metric whose Levi-Civita connection coincides with the canonical connection of the bi-Lagrangian manifold.