Can some one find a surface that has positive constant curvature that is not open subset of sphere.
I know every connected and compact surface with positive constant curvature is sphere.
I need some hint. Thanks a lot indeed
2026-04-23 21:58:36.1776981516
Find a surface that has positive constant curvature that is not open subset of sphere
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HINT: You can write down the expression for the Gaussian curvature of a general surface of revolution. For example, assume it's obtained by rotating the arclength parametrized curve $x=f(s)$, $z=g(s)$ about the $z$-axis. Then you should be able to show that $f''(s)+Kf(s)=0$. You will get plenty of surfaces of constant curvature (including, but not limited to, spheres).