Geometry of Certain Lie-Frobenius Groups
Differential Geometry
2016-08-16 v1
Abstract
We study the geometry of a family of Lie groups, which contained the classical affine Lie groups, endowed with an exact left invariant symplectic form. We show that this family is closed by symplectic reduction and symplectic double extension in the sense of Dardi\'{e} and Medina. We prouve also that these groups are endowed with two transverse left invariant Lagrangian (resp. Symplectic) foliations. This implies that these groups admit a left invariant torsion free symplectic connection.
Cite
@article{arxiv.math/0506365,
title = {Geometry of Certain Lie-Frobenius Groups},
author = {Jean Michel Dardie and Alberto Medina and Hassène Siby},
journal= {arXiv preprint arXiv:math/0506365},
year = {2016}
}
Comments
13 pages