2) complete noncompact Riemannian manifold
完备非紧黎曼流形
1.
It is well-known that there is a unique vertex on rotating parabolic surface in three-dimensional Euclidiean space,the paper generalizes the concept of vertex to a complete noncompact Riemannian manifold with nonnegative curvature.
将三维欧式空间旋转抛物面顶点的定义推广到一般的非负曲率完备非紧黎曼流形上,利用Perelman G证明Chee-ger-Gromoll核心猜想的几何方法,讨论了具非负曲率的完备非紧黎曼流形M上的核心S的结构,证明了如果由核心出发的法测地线均为射线,则或者S退化为一点,或者M=Rk×N,其中N是紧致的具非负曲率的黎曼流形。
2.
The paper discusses the structure of the soul in a complete noncompact Riemannian manifold M with nonnegative curvature,and proves that if the soul of the manifold is unique,then the soul actually degenerates to a pole.
讨论了具非负曲率的完备非紧黎曼流形上的核心的结构,证明了如果核心是惟一的,那么核心将退化为极点。
3.
The parallel properties of the rays in a complete noncompact Riemannian manifoldM were discussed in this paper, It is proved that the Busemann functions corresponding to any given two parallel rays are just the same as each other in the sense of H.
讨论了具非负典率的完备非紧黎曼流形M上平行射线的性质,证明了此时两平行射线对应于M上的同一个Busemann函数。
3) normal complete open riemannian manifold
完备非紧正则黎曼流形
4) Non-compact flow
非紧致流
1.
Non-compact flow is a special flow that exists in non-compact metric space.
非紧致流是存在于非紧致度量空间上的一类特殊的流，本文通过悬撑的概念提出一种由离散流构造连续非紧致流的方法。
2.
According to the concept of topological chain recurrent ,a special flow “non-compact flow” is introduced on metric space, some properties and examples of this flow are given.
通过拓扑链回归概念，在非紧致度量空间中引入一类特殊的流———非紧致流，同时给出该类流的一些特性和实例。
5) compact manifold
紧流形
1.
The paper studies some nonlinear optimal control,proves the existence of a Kalman-Riccati matrix differential equation on a compact manifold,which is represented via local coordinates,and its solution in local coordinates is bound,symmetric positive matrix function.
从一类非线性最优控制问题出发,证明了一类在局部坐标表示下紧流形上Kalm an-R iccati矩阵微分方程解的存在性,并证明其解在局部坐标下是有界对称正定矩阵函数。
补充资料：紧可解流形
紧可解流形
soft manifold, compact
紧可解流形〔劝h Irla抽创d，卿钾d或comPact sofv-mall而ld;pa3pe川加Moe Muoro06pa3oe」 连通可解L记群的一个紧的商空间(见可解lje群(球grouP，solvable);然而，有时紧性不是必须的).一个特殊的情形是诣零流形(成仃皿川-fold).与后者相比，一般情况可考虑得更复杂，但对它也存在完全结构理论.【补注】也见可解流形(solv mainfokl).
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