Dirac brackets and reduction of invariant bi-Poisson structures

Ihor V. Mykytyuk, Andriy Panasyuk

Let $X$ be a manifold with a bi-Poisson structure $\{{\eta }^t\}$ generated by a pair of $G$-invariant symplectic structures ${\omega }_1$ and ${\omega }_2$, where the Lie group $G$ acts properly on $X$…