symplectization造句

例句与造句

This new manifold is called the symplectization ( sometimes symplectification in the literature ) of the contact manifold " M ".
For instance, in symplectic Floer homology, one considers the product of the mapping torus of a symplectomorphism with the real numbers; in symplectic field theory, one considers the symplectization of a contact manifold.
When the contact structure \ xi is cooriented by means of a contact form \ alpha, there is another version of symplectization, in which only forms giving the same coorientation to \ xi as \ alpha are considered:
Its generators are Reeb chords, which are trajectories of the Reeb vector field beginning and ending on a Lagrangian, and its differential counts certain holomorphic strips in the symplectization of the contact manifold whose ends are asymptotic to given Reeb chords.
It is a fact that any contact manifold ( " M ", ? ) can be embedded into a canonical symplectic manifold, called the symplectization of " M ", such that " M " is a contact type level set ( of a canonically defined Hamiltonian ) and the Reeb vector field is a Hamiltonian flow.