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Let $(M,g)$ be a Riemannian manifold with isometric group $G=Iso(M,G)$. The metric gives an isomorphism between tangent and cotangent bundle of $M$. So $g$ induce a natural symplectic structure on $...

Let $G$ be a compact Lie group with Lie algebra $\mathfrak{g}$. Let $<.,>$ denote a $G$-invariant inner product on $\mathfrak{g}$. Let $(M,\omega)$ be a symplectic compact manifold endowed with ...

Let $G$ be a compact connected Lie group acting in a Hamiltonian fashion on a symplectic manifold $M$ with momentum map $\mu:M\to \mathfrak{g}^\ast$, where $\mathfrak{g}$ is the Lie algebra of $G$. ...