1) Surface with negative Gauss Curvature
负曲率曲面
2) curved surface with negative gauss curvature
负高斯曲率曲面
3) 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。
4) negative curvity
常负曲率
1.
Based on the idea of integrable system,taking advantage of matrix model for 3-dimensional Minkowski space L 3,the integrability and curved suface deformation of negative curvity in L 3 were studied.
利用可积系统的思想 ,借助三维Minkowski空间L3的矩阵模型 ,我们研究了L3中常负曲率的类空曲面的形变及其可积性。
6) curved surface of high curvature
大曲率曲面
补充资料：常曲率曲面
| 常曲率曲面 constant curvature，surface of 总曲率（或高斯曲率）在整个曲面上为常数的曲面。总曲率是曲面的两个主曲率的乘积。常数平均曲率曲面是其平均曲率在整个曲面上为常数的曲面，在这里平均曲率定义为主曲率的平均值，半径为r的球面有常数总曲率1／r2和常数平均曲率2／r。 |
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