Quadratic Differentials, Quaternionic Forms, and Surfaces
| dc.creator | Kamberov, George I. | |
| dc.date | 1997-12-21 | |
| dc.date | 1997-12-30 | |
| dc.date.accessioned | 2026-07-07T03:24:38Z | |
| dc.date.available | 2026-07-07T03:24:38Z | |
| dc.description | Global isothermic immersions are defined and studied with the aid of a connection between quadratic differentials and immersions. The applications are two problems stemming from the fundamental question: how much data is needed to identify a surface immersion (Christoffel's problem) or its shape (Bonnet's problem). A short complete solution of Christoffel's problem, including closed surfaces, is given. It is shown that every immersion of an oriented closed surface (genus $\neq$ 1) is uniquely determined up to similitude by its conformal class and the tangent planes map. A classification of all generic Bonnet surfaces follows from a series of papers by Bonnet, Cartan, and Chern. The existence of a new class of Bonnet surfaces is shown here. The understanding of this class is necessary in order to study the rigidity of closed surfaces. | |
| dc.description | LaTeX. Stylistic changes and spelling mistakes corrected. Definitions 2 and 3, and Remark 4 are streamlined | |
| dc.identifier | https://arxiv.org/abs/dg-ga/9712011 | |
| dc.identifier | http://arxiv.org/abs/dg-ga/9712011 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/33402 | |
| dc.subject | Differential Geometry | |
| dc.subject | 53A05;53A55;53C42;35F25 | |
| dc.title | Quadratic Differentials, Quaternionic Forms, and Surfaces | |
| dc.type | text |