Timeline for Surfaces with non-constant negative curvature
Current License: CC BY-SA 4.0
3 events
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| May 5, 2020 at 7:19 | comment | added | Sebastian | Hi Andy, I see your point. On the other hand we do not have an extrinsic model for the hyperbolic ball in 3-space as well, and the explicit form for the metric of a minimal surface is given on the domain of the conformal parametrisation. Of course, one can ask which complete embedded examples without umbilics do exist. But even with the further constraint of finite total curvature we have at least one (class of) example(s). | |
| May 4, 2020 at 19:54 | comment | added | Andy Sanders | Hey Sebastian, you're certainly right that generally speaking the Enneper-Weierstrass parameterization is a nice way to generate examples of negatively curved surfaces. But, they do tend to be immersed and therefore extrinsic in nature, so they are quite different than the kind of model that the Poincare disk is. Still, this is a nice class of examples. | |
| May 4, 2020 at 16:11 | history | answered | Sebastian | CC BY-SA 4.0 |