On symmetries of constant mean curvature surfaces
| dc.creator | Dorfmeister, Josef | |
| dc.creator | Haak, Guido | |
| dc.date | 1996-03-14 | |
| dc.date | 1996-03-19 | |
| dc.date.accessioned | 2026-07-07T09:02:48Z | |
| dc.date.available | 2026-07-07T09:02:48Z | |
| dc.description | We start the investigation of immersions $Ψ$ of a simply connected domain $D$ into three dimensional Euclidean space $R^3$, which have constant mean curvature (CMC-immersions), and allow for a group of automorphisms of $D$ which leave the image $Ψ(D)$ invariant. On one hand, this leads to a detailed description of symmetric CMC-surfaces and the associated symmetry groups. On the other hand, it allows us to start the classification of CMC-immersions of an arbitrary, compact or noncompact Riemann surface $M$ into $R^3$ in terms of Weierstrass-type data, as introduced by Pedit, Wu, and one of the authors [D]. We use our general results to prove, that there are no CMC-tori or Delaunay surfaces in the dressing orbit of the cylinder. As an example, we apply the discussion to Smyth surfaces and to a CMC-surface with a branchpoint. | |
| dc.description | 42 pages, LaTeX, no figures, revision correcting several misprints | |
| dc.identifier | https://arxiv.org/abs/dg-ga/9603007 | |
| dc.identifier | http://arxiv.org/abs/dg-ga/9603007 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/148766 | |
| dc.subject | Differential Geometry | |
| dc.title | On symmetries of constant mean curvature surfaces | |
| dc.type | text |