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Jacobi actions of \(SO(2)\times\mathbb{R}^ 2\) and \(SU(2,\mathbb{C})\) on two Jacobi manifolds. (English) Zbl 0842.57034
The actions of two subgroups of \(\text{SO} (2) \times \mathbb{R}\) on a sphere of the dual space \(G^* = (\text{so} (2) \times \mathbb{R})^*\) with the Jacobi manifold structure obtained as quotient by the homothety group of the Lie-Poisson structure in \(G^* \smallsetminus \{0\}\) are studied. It is shown that the natural action of \(\text{SU} (2, \mathbb{C})\) on the unitary 3-sphere of \(\mathbb{C}^2\) with the Jacobi structure determined by its canonical contact structure is a Jacobi action that admits a unique \(\text{Ad}^*\)-equivariant momentum mapping (in the sense of J.-M. Sourian and B. Konstant).
Reviewer: M.Rahula (Tartu)
MSC:
57S25 Groups acting on specific manifolds
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