Timeline for "Famous" 2d Riemannian manifolds with non-constant curvature
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
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| Apr 29, 2011 at 17:06 | comment | added | Deane Yang | The torus is unlikely to be conformal to the Poincare disk, and I doubt the paraboloid is, either. However, the helicoid (which is the universal cover of the catenoid) and the Enneper surface probably are. If I had to guess, any complete immersed minimal surface with Gauss curvature bounded from above by a negative constant is conformally equivalent to the Poincare disk. But that's just a guess. | |
| Apr 29, 2011 at 16:34 | comment | added | Daniel | Are any of these deformations of the Poincare disc? (I should have added that ideally I'm looking for "famous" one or two parameter deformations of the Poincare disc such that the deformation introduces the non-constant curvature.) | |
| Apr 29, 2011 at 13:45 | comment | added | Willie Wong | I didn't know about the Enneper surface. Thanks for showing me something new. | |
| Apr 29, 2011 at 1:25 | history | answered | Deane Yang | CC BY-SA 3.0 |