For the cotangent bundle of a smooth Riemannian manifold acted upon by the lift of a smooth and proper action by isometries of a Lie group, we construct a Witt-Artin decomposition at any point. We also obtain a splitting of the symplectic normal space which is related to the original bundle structure. This splitting is computed only in terms of the group… (More)
For the cotangent bundle T * Q of a smooth Riemannian manifold acted upon by the lift of a smooth and proper action by isometries of a Lie group, we characterize the symplectic normal space at any point. We show that this space splits as the direct sum of the cotangent bundle of a linear space and a symplectic linear space coming from reduction of a… (More)
We apply geometric techniques to obtain the necessary and sufficient conditions on the existence and nonlinear stability of self-gravitating Rie-mann ellipsoids having at least two equal axes.
We address the problem of computing the fundamental group of a symplectic S 1-manifold for non-Hamiltonian actions on compact manifolds, and for Hamiltonian actions on non-compact manifolds with a proper moment map. We generalize known results for compact manifolds equipped with a Hamiltonian S 1-action. Several examples are presented to illustrate our main… (More)