Mean curvature 1 Enneper cousins and their duals in hyperbolic 3-space. (English) Zbl 1175.53014
Summary: We show a mean curvature 1 Enneper cousin in hyperbolic 3-space. (Hyperbolic 3-space is shown here using the Poincaré model.) This surface is isometric to the minimal Enneper surface in Euclidean 3-space. The second surface we show is the dual surface to the Enneper cousin shown here. Only one of four congruent pieces, with the end cut away, of each surface is shown.
MSC:
| 53A10 | Minimal surfaces in differential geometry, surfaces with prescribed mean curvature |
| 53A35 | Non-Euclidean differential geometry |
| 53C42 | Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) |
