Jacobi Actions of $\SO(2)\times\R^{2}$ and $\SU(2,\C)$ on Two Jacobi Manifolds

Joana Margarida Nunes da Costa

Abstract: We take a sphere $S$ of the dual space $\calc{G}^{*}$ of $\calc{G}=\so(2)\times\R^{2}$ with the Jacobi manifold structure obtained by quotient by the homothety group of the Lie-Poisson structure in $\calc{G}^{*}\backslash\{0\}$ and we study the actions of two subgroups of $\SO(2)\times\R^{2}$ on $S$.
We show that the natural action of $\SU(2,\C)$ on the unitary 3-sphere of $\C^{2}$ with the Jacobi structure determined by its canonical contact structure is a Jacobi action that admits an unique $\Ad^{*}$-equivariant momentum mapping.

Full text of the article:

• Compressed PostScript file (84 kilobytes)
• PDF file (160 kilobytes)