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Show that there is no metric on S^2 having curvature bounded above by 0 and no metric on surface of genus g which is bounded below by 0.

honestly I have no idea what is going on here. I know that a Genus is the number of holes in some manifold or the number of cuts performed that will not leave the manifold disconnected. Also a metric, such as the distance - although I don't understand how it is applied here. But most of all, I have no idea what the point is and how it is the bounding even happens.

Note: this is not homework but a question in a list to study for an exam - so I am hoping to understand the intuition and how to even generalize this to something else.

Thanks, any help is much appreciated.

Brian