1) parallel vectors
平行向量
2) parallel vector field
平行向量场
1.
The paper discusses the relations between parallel vector fields and Jacobi fields in a complete Riemannian manifold, and proves that there exists infinite closed geodesics in a local symmetric space which is orientable, compact, nonsimply connected and with nonnegative sectional curvature.
讨论了曲率定号的完备黎曼流形上的平行向量场与Jacobi场之间的关系;证明了紧致的偶数维具非负曲率的非单连通局部对称空间上存在无穷多条长度一样的闭测地线。
3) vectors/parallel mean currature vector
向量/平行平均曲率向量
4) antiparallel
[,ænti'pærəlel]
反向平行，逆平行(矢量)
5) parallel normal vector field
平行法向量场
6) pararrel mean curvature vector
平行中曲率向量
1.
This paper considers submanifold with pararrel mean curvature vector and positive curvature in a unit sphere,and we get a pinching theorem of the length of Riemanian curvature tensor.
本文讨论了单位球面Sn+p中的具有平行中曲率向量的紧致正曲率子流形,给出了一个关于黎曼曲率张量长度平方的pinching定理。
2.
At first, this paper considers submanifold with pararrel mean curvature vector and positive scalar curvature in a sphere, make use of the sphere of the length of the Riemanian curvature tensor, some in.
关于球面中紧致极小子流形某些曲率的Pinching问题,即通常所谓的内蕴刚性,文[1],[2],[3],[4]已经有了许多好的结果,这些结果大部分是用第二基本形式模长的平方,截面曲率,Ricci曲率来刻画的,本文首先讨论了球面中具有平行中曲率向量的紧致正截面曲率子流形,通过对子流形的黎曼曲率张量长度平方的限制,得到了球面中该类子流形的一些性质。
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