We consider a connected symplectic manifold $M$ acted on properly and in a Hamiltonian fashion
by a connected Lie group $G$. If $G$ is compact, then we characterize the symplectic manifolds whose
squared moment map is constant.
We also give a sufficient condition for $G$ to admit a symplectic orbit. Then we study the case when $G$ is a non-compact Lie group
proving splitting results for symplectic manifolds.
Publié le : 2009-02-15
Classification:
moment map,
symplectic and almost-Kähler manifolds,
53C55,
57S15
@article{1235574195,
author = {Biliotti, Leonardo},
title = {On the moment map on symplectic manifolds},
journal = {Bull. Belg. Math. Soc. Simon Stevin},
volume = {16},
number = {1},
year = {2009},
pages = { 107-116},
language = {en},
url = {http://dml.mathdoc.fr/item/1235574195}
}
Biliotti, Leonardo. On the moment map on symplectic manifolds. Bull. Belg. Math. Soc. Simon Stevin, Tome 16 (2009) no. 1, pp. 107-116. http://gdmltest.u-ga.fr/item/1235574195/