1. CMB 2011 (vol 54 pp. 716)
|Symplectic Lie-Rinehart-Jacobi Algebras and Contact Manifolds|
We give a characterization of contact manifolds in terms of symplectic Lie-Rinehart-Jacobi algebras. We also give a sufficient condition for a Jacobi manifold to be a contact manifold.
Keywords:Lie-Rinehart algebras, differential operators, Jacobi manifolds, symplectic manifolds, contact manifolds
Categories:13N05, 53D05, 53D10
2. CMB 2003 (vol 46 pp. 277)
|Rigidity of Hamiltonian Actions |
This paper studies the following question: Given an $\omega'$-symplectic action of a Lie group on a manifold $M$ which coincides, as a smooth action, with a Hamiltonian $\omega$-action, when is this action a Hamiltonian $\omega'$-action? Using a result of Morse-Bott theory presented in Section~2, we show in Section~3 of this paper that such an action is in fact a Hamiltonian $\omega'$-action, provided that $M$ is compact and that the Lie group is compact and connected. This result was first proved by Lalonde-McDuff-Polterovich in 1999 as a consequence of a more general theory that made use of hard geometric analysis. In this paper, we prove it using classical methods only.