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1·It is locally convex in the sense that it has no loops and the curvature never changes sign.

它的局部是凸的，因为它没有环路，且曲率永远不会改变符号。

2·The hyperbolic surface, which has so-called negative curvature because its surface curves up and down at the same time, like a saddle.

双曲曲面，即通常所称的负曲率，因为它的表面同时向上和向下弯曲，就像一个马鞍。

3·Curvature of the surface prevents slump block from becoming completely detached.

表面的曲率防止滑塌块完全脱离。

4·If the universe has a positive curvature, it's a closed universe.

正曲率的宇宙是封闭的宇宙。

5·It goes back... Actually, some of you may be able to see the curvature.

它回来了。，事实上，你们有些人，也许能看到曲率。

6·Matter, energy and dark energy all produce curvature in space-time, however.

而事实上，物质、能量和暗能量在时空中都会产生弯曲。

7·Any farther away, and the system encounters problems due to the curvature of the earth.

由于地球表面弯曲，距离更远时，系统就遇到问题。

8·Because at that height you can see the blackness of space and the curvature of the earth.

因为在那个高度你可以看到太空的漆黑和地球的轮廓。

9·Technically, it occurs when the rate of curvature between 2 continuous surfaces are the same.

从技术上讲，当两个连续曲面拥有同样的曲率时才会出现。

10·Negative curvature is a little trickier to visualize. The most common description is a saddle.

了解负曲率宇宙要动点脑筋，最常见的描述就是它像马鞍。

(1)curvature radius曲率半径

(1)radius of curvature曲率半径

(1)mean curvature平均曲率

(1)gaussian curvature高斯曲率

(1)constant curvature常曲率

(1)field curvature场曲率