讨论了紧致非单连通的具非负曲率的流形的一些几何性质，并应用它们证明了具非负曲率的紧致非单连通曲面必为平坦的。
With the help of them, it can be proved that the non-simply connected compact surface with nonnegative curvature must be flat.
在这个例子里，圈饼表面就是非单连通的，并且这类物体的简化就会像是至少有一个洞的曲面。
In this example, the surface is not simply connected and any smoothed-out object looks like a torus with at least one hole.
单连通和非单连通的概念，研究哪些环路能界定曲面，可以用来对空间内部物体的形状进行分类。
This concept of being simply connected or not, and studying which loops bound surfaces or not can be used to classify shapes of things inside space.
首先，本文基于连续边缘曲面的连通特性，提出了一个三维图像中阶梯型边缘曲面的检测与追踪算法。
Firstly, a new surface detecting and tracing algorithm is proposed in this dissertation based the connectivity characteristics of the edge surface.
首先，本文基于连续边缘曲面的连通特性，提出了一个三维图像中阶梯型边缘曲面的检测与追踪算法。
Firstly, a new surface detecting and tracing algorithm is proposed in this dissertation based the connectivity characteristics of the edge surface.
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