1) nonnegative curvature
非负曲率
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 gathers some results in Riemannian manifolds,including in complete geodesics without conjugate points,the geometric struture of a manifold with nonnegative curvature,the topology of a manifold with nonnegative Ricci curvature and some properties of Busemann function etc.
总结了完备黎曼流形上完备的无共轭点测地线所隐含的几何性质、完备非紧具非负曲率黎曼流形的几何结构、完备非紧具非负R icc i曲率黎曼流形的几何拓扑性质以及完备非紧黎曼流形上的Buse-m ann函数所隐含的几何拓扑性质,并提出了一些未解决的问题。
3.
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。
2) Nonnegative Ricci curvature
非负Ricci曲率
1.
The topology of complete manifolds with nonnegative Ricci curvature and large volume growth;
具非负Ricci曲率和大体积增长的完备流形的拓扑(英文)
2.
For an open complete Riemannian manifold with nonnegative Ricci curvature,the present paper discusses the relation between the topology and the volume growth.
本文讨论了具非负Ricci曲率的完备非紧黎曼流形的体积增长与其拓扑性质之间的关系。
3.
By comparing the volume growth order of the manifold itself to that of its universal covering space, the paper proves that every three-dimensional with nonnegative Ricci curvature and (1+δ)-order volume growth in strict sense must be contractible provided that its universal covering is finite.
本文研究了三维完备非紧具非负Ricci曲率的黎曼流形的几何拓扑性质。
3) asymptotically nonnegative curvature
渐进非负曲率
1.
In the paper, we used some types of asymptotically nonnegative curvature to get some conditions of complete noncompact Riemannian manifold which is nonparabolic.
在本文中,主要讨论完备非紧的黎曼流形的Green函数的性质,主要利用各种渐进非负曲率和体积条件,得到在不同条件下流形是非抛物的结果。
4) nonnegative Gauss curvature
非负高斯曲率
5) quadratically nonnegatively curved infinity
渐近非负曲率
1.
By Buseman function,the author discusses the geometry and topology of a complete manifolds with quadratically nonnegatively curved infinity.
讨论了具二次渐近非负曲率完备非紧黎曼流形上的Busemann函数所隐含的几何拓扑性
6) almost nonnegative Ricci curvature
几乎非负Ricci曲率
补充资料：非想非非想处天
1.佛教语。即三界中无色界第四天。此天没有欲望与物质﹐仅有微妙的思想。
说明：补充资料仅用于学习参考，请勿用于其它任何用途。
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