Every symplectic manifold is even dimensional. This is easy to understand in view of the physics. In Hamilton equations, location and momentum vectors always appear in pairs.
A form on a -dimensional manifold is non-degenerate if and only if the -fold product is non-zero.
As a consequence of the last , every symplectic manifold is orientable.
Let and be symplectic manifolds. Then a diffeomorphism is called a symplectomorphism if , that is, if the symplectic form on pulls back to the form on .
A symplectomorphism is also known as a canonical transformation. This is mostly used in the mechanics literature.
|Date of creation||2013-03-22 13:12:18|
|Last modified on||2013-03-22 13:12:18|
|Last modified by||matte (1858)|