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.

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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.

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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.

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