Portugaliæ Mathematica   EMIS ELibM Electronic Journals PORTUGALIAE
Vol. 52, No. 1, pp. 95-107 (1995)

Previous Article

Next Article

Contents of this Issue

Other Issues

ELibM Journals

ELibM Home



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

Joana Margarida Nunes da Costa

Departamento de Matemática,
Apartado 3008, 3000 Coimbra - PORTUGAL

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:

Electronic version published on: 29 Mar 2001. This page was last modified: 27 Nov 2007.

© 1995 Sociedade Portuguesa de Matemática
© 1995–2007 ELibM and FIZ Karlsruhe / Zentralblatt MATH for the EMIS Electronic Edition