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 2001 (vol 44 pp. 129)
|LinÃ©arisation symplectique en dimension 2 |
In this paper the germ of neighborhood of a compact leaf in a Lagrangian foliation is symplectically classified when the compact leaf is $\bT^2$, the affine structure induced by the Lagrangian foliation on the leaf is complete, and the holonomy of $\bT^2$ in the foliation linearizes. The germ of neighborhood is classified by a function, depending on one transverse coordinate, this function is related to the affine structure of the nearly compact leaves.
Keywords:symplectic manifold, Lagrangian foliation, affine connection