How to prove the following:
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 $0$.
How to prove the following:
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 $0$.