The Weierstrass representation of spheres in $R^3$, the Willmore numbers, and soliton spheres
| dc.creator | Taimanov, Iskander A. | |
| dc.date | 1998-01-07 | |
| dc.date | 1998-01-08 | |
| dc.date.accessioned | 2026-07-07T05:23:30Z | |
| dc.date.available | 2026-07-07T05:23:30Z | |
| dc.description | The Weierstrass representation for spheres in $\R^3$ and, in particular, effective construction of immersions from data of spectral theory origin is discussed. These data are related to Dirac operators on a plane and on an infinite cylinder and these operators are just representations of Dirac operators acting in spinor bundles over the two-sphere which is naturally obtained as a completion of a plane or of a cylinder. Spheres described in terms of Dirac operators with one-dimensional potentials on a cylinder are completely studied and, in particular, for them a lower estimate of the Willmore functional in terms of the dimension of the kernel of the corresponding Dirac operator on a two-sphere is obtained. It is conjectured that this estimate is valid for all Dirac operators on spheres and some reasonings for this conjecture are discussed. In Appendix a criterion distinguishing Weierstrass representations, of universal coverings of compact surfaces of higher genera, converted into immersions of compact surfaces is given. | |
| dc.description | 30 pages, LaTeX; Preprint no. 302, SFB 288, TU-Berlin | |
| dc.identifier | https://arxiv.org/abs/math/9801022 | |
| dc.identifier | http://arxiv.org/abs/math/9801022 | |
| dc.identifier | Proceedings of the Steklov Institute of Math. 225 (1999), 222-243. | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/76462 | |
| dc.subject | Differential Geometry | |
| dc.title | The Weierstrass representation of spheres in $R^3$, the Willmore numbers, and soliton spheres | |
| dc.type | text |