辛流形上向量场的一些性质

Some Properties of Vector Fields on Symplectic Manifolds

在辛流形（Ｍ，ω）的向量场李代数Ｃ∞（Ｍ，ＴＭ）中定义了一种算子Ｐ：Ｃ∞（Ｍ，ＴＭ）×Ｃ∞（Ｍ，ＴＭ）→Ｃ∞（Ｍ，ＴＭ），得到了向量场是辛向量场的一个简明的充要条件，同时还得到了一些有关辛向量场与Ｈａｒｍｉｌｔｏｎ向量场的恒等式．

Defines an opertor P: C∞ (M,TM) × C∞ (M,TM) → C∞ (M,TM) in vector field Lie algebra Coo (M,TM) on symplectic manifold (M,co) and gets as simple sufficient and nesessary condition for the vector fields being symplectic vector fields, and also obtains some identities on symplectic and Harmilton vector fields.