1) left invariant symplectic structure
辛左不变向量场
1.
On the basis of paper [4],the equivalence of the necessary and sufficient conditions is proved,and local coordinate representations of left invariant symplectic structure and symplectic left invariant vector field on the Symplectic-Lie group are given.
在文[4]的基础上,证明了X∈S(G,dω)的两个充要条件的等价性,还给出了辛李群上左不变辛结构和辛左不变向量场的局部坐标表示。
2) Left invariant vector field
左不变向量场
1.
In the paper, we discuss the relations among the left invariant vector field, the parallel vector field and the Jacobi field, get a sufficient and necessary condition for a Lie group to be flat.
讨论了李群Ｇ上的左不变向量场、平行向量场与Ｊａｃｏｂｉ场之间的关系，得到了Ｇ为平坦的一个充要条件。
3) symplectic vector field
辛向量场
1.
In this paper,first of all , we establish a necessary and sufficient condition that a vector X on the cotangent bundle T*P is symplectic vector fields.
文中先建立了余切丛TP上向量场X为辛向量场的充要条件,以此为据,给出了一系列具体的向量场是或不是辛向量场的判断。
2.
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.
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。
4) local coordinate representation
左不变辛结构
1.
On the basis of paper [4],the equivalence of the necessary and sufficient conditions is proved,and local coordinate representations of left invariant symplectic structure and symplectic left invariant vector field on the Symplectic-Lie group are given.
在文[4]的基础上,证明了X∈S(G,dω)的两个充要条件的等价性,还给出了辛李群上左不变辛结构和辛左不变向量场的局部坐标表示。
5) pseudometric left-invariant
伪度量左不变量
6) symmetric groups/invariant vector fields
对称群/不变向量场
补充资料：Jacobi向量场
Jacobi向量场
Jacoin vector field
Jaa无i向量场[而“肠，“为贾五dd;只劝6“"o胎] 沿测地线(即司“ic五Ile)满足加伽俪方程(Jacobi叫之左山。n)的向量场，沈一兵译
说明：补充资料仅用于学习参考，请勿用于其它任何用途。
参考词条