The number of constant mean curvature isometric immersions of a surface
| dc.creator | Smyth, Brian | |
| dc.creator | Tinaglia, Giuseppe | |
| dc.date | 2008-11-10 | |
| dc.date | 2008-11-14 | |
| dc.date.accessioned | 2026-07-07T10:17:56Z | |
| dc.date.available | 2026-07-07T10:17:56Z | |
| dc.description | In classical surface theory there are but few known examples of surfaces admitting nontrivial isometric deformations and fewer still non-simply-connected ones. We consider the isometric deformability question for an immersion x: M \to R^3 of an oriented non-simply-connected surface with constant mean curvature H. We prove that the space of all isometric immersions of M with constant mean curvature H is, modulo congruences of R^3, either finite or a circle. When it is a circle then, for the immersion x, every cycle in M has vanishing force and, when H is not 0, also vanishing torque. Our work generalizes a rigidity result for minimal surfaces to constant mean curvature surfaces. Moreover, we identify closed vector-valued 1-forms whose periods give the force and torque. | |
| dc.description | 21 pages, 1 figure. This paper is now dedicated to Katsumi Nomizu and the references have been updated | |
| dc.identifier | https://arxiv.org/abs/0811.1231 | |
| dc.identifier | http://arxiv.org/abs/0811.1231 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/174029 | |
| dc.subject | Differential Geometry | |
| dc.subject | 53A10 | |
| dc.title | The number of constant mean curvature isometric immersions of a surface | |
| dc.type | text |