Bi-Lagrangian structures on nilmanifolds
Symplectic Geometry
2019-03-01 v2 Differential Geometry
Abstract
We study bi-Lagrangian structures (a symplectic form with a pair of complementary Lagrangian foliations, also known as para-K\"ahler or K\"unneth structures) on nilmanifolds of dimension less than or equal to 6. In particular, building on previous work of several authors, we determine which 6-dimensional nilpotent Lie algebras admit a bi-Lagrangian structure. In dimension 6, there are (up to isomorphism) 26 nilpotent Lie algebras which admit a symplectic form, 16 of which admit a bi-Lagrangian structure and 10 of which do not. We also calculate the curvature of the canonical connection of these bi-Lagrangian structures.
Cite
@article{arxiv.1810.06518,
title = {Bi-Lagrangian structures on nilmanifolds},
author = {M. J. D. Hamilton},
journal= {arXiv preprint arXiv:1810.06518},
year = {2019}
}
Comments
23 pages; to appear in J. Geom. Phys