Timeline for Can you have a spherical plane?
Current License: CC BY-SA 2.5
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| Apr 16, 2010 at 8:55 | comment | added | Gunnar Þór Magnússon | Really? But it needs to be non-orientable, right? My understanding is that if not you can put some almost complex structure compatible with the metric on the surface. This structure will automatically be integrable, so we have a Riemann surface with a metric of constant positive curvature. Thus its universal cover is $\mathbb P^1$, and the only thing covered by the sphere is the sphere itself. Does this line of reasoning go wrong somewhere? | |
| Apr 15, 2010 at 17:14 | comment | added | Qfwfq | @Gunnar: a non-complete surface of constant positive curvature is not necessarily diffeomorphic to a sphere. | |
| Apr 15, 2010 at 16:43 | history | answered | Gunnar Þór Magnússon | CC BY-SA 2.5 |