Geometry of Certain Lie-Frobenius Groups

Details Geometry of Certain Lie-Frobenius Groups Geometry of Certain Lie-Frobenius Groups

2005-06-18

arxiv.org/abs/math/0506365v1

Mathematics

Differential Geometry

13 pages

Scientific paper

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.

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