Willmore Surfaces of Constant Moebius Curvature
| dc.creator | Ma, Xiang | |
| dc.creator | Wang, Changping | |
| dc.date | 2006-09-04 | |
| dc.date | 2006-09-18 | |
| dc.date.accessioned | 2026-07-07T08:28:52Z | |
| dc.date.available | 2026-07-07T08:28:52Z | |
| dc.description | We study Willmore surfaces of constant Moebius curvature $K$ in $S^4$. It is proved that such a surface in $S^3$ must be part of a minimal surface in $R^3$ or the Clifford torus. Another result in this paper is that an isotropic surface (hence also Willmore) in $S^4$ of constant $K$ could only be part of a complex curve in $C^2\cong R^4$ or the Veronese 2-sphere in $S^4$. It is conjectured that they are the only examples possible. The main ingredients of the proofs are over-determined systems and isoparametric functions. | |
| dc.description | 16 pages. Mistakes occured in the proof to the main theorem (Thm 3.6) has been corrected | |
| dc.identifier | https://arxiv.org/abs/math/0609057 | |
| dc.identifier | http://arxiv.org/abs/math/0609057 | |
| dc.identifier | Annals of Global Analysis and Geometry 32(2007), No.3, 297-310 | |
| dc.identifier | doi:10.1007/s10455-007-9065-9 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/137771 | |
| dc.subject | Differential Geometry | |
| dc.subject | 53A30 (53C21, 53C24, 53C42) | |
| dc.title | Willmore Surfaces of Constant Moebius Curvature | |
| dc.type | text |