1) 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。
2) 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。
3) normal field
法向量场
1.
Triangulation mesh generation of scatter points based on normal field;
基于法向量场的散乱点集三角网格化
4) Hamilton vector field
Hamilton向量场
1.
A class of perturbed cubic Z2-equivariant Hamilton vector field is discussed in this paper.
考虑一类扰动的平面三次Z2-等变Hamilton向量场,借助数值分析工具,利用平面动力系统分支理论和判定函数方法证明该向量场至少存在11个极限环,且给出这些极限环的相对位置分布。
2.
In this paper,Some properties of product poisson manifold are discussed,some formulas of Hamilton vector field are also obtained;Morover,the Concept of Poisson Group is introduced in this paper and is applied in poisson manifol
本文讨论了Poisson积流形的一些性质,得出了Hamilton向量场的若干公式;文中还引入Poisson群的概念,并给出了它在Poisson流形中的应用。
5) vector fields
向量场
1.
Existence of singular point and vector fields for the force of crust;
地壳受力的向量场及奇点的存在性
2.
It is studied that smooth linearizability and finitely smooth linearizability of some hyperbolic vector fields.
讨论了一类向量场X(x) =Ax +…在双曲奇点附近的光滑线性化及有限阶光滑线性化问题。
3.
An index formula of singularities of vector fields on manifolds with boundary due to M.
Morse关于带边流形上向量场的奇点指标公式 ,应用延拓形变成adapted场的方法 ,给出了该公式一个更为简洁本质的证明 ,得到Rn 中单连通区域上连续映射的孤立零点估计 。
6) Hopf vector field
Hopf向量场
1.
With a Sasaki metric defined by Hopf vector field,we show that the Hopf vector field has minimum volume on S2n+1 for all n.
采用切丛TS2n+1上的不同联络,证明了Hopf向量场是S2n+1上体积最小的单位向量场。
2.
In particular, we get Sasaki metric on unit tangent bundle T_1S~(2n+1), by which we calculate the volume of the Hopf vector field V_h.
在此度量下计算了奇数维球面S~(2n+1)上Hopf向量场V_H的体积，由Gysin序列得到了T_1S~(2n+1)的上同调群。
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