Minimal Tori in $S^3$
| dc.creator | Carberry, Emma | |
| dc.date | 2004-07-16 | |
| dc.date | 2007-04-09 | |
| dc.date.accessioned | 2026-07-07T09:39:28Z | |
| dc.date.available | 2026-07-07T09:39:28Z | |
| dc.description | We prove existence results that give information about the space of minimal immersions of 2-tori into $ S ^ 3 $. More specifically, we show that \begin{enumerate} \item For every positive integer $ n $, there are countably many real $n $-dimensional families of minimally immersed 2-tori in $ S ^ 3 $. Every linearly full minimal immersion $ T ^ 2\to S ^ 3 $ belongs to exactly one of these families. \item Let $ \mathcal A $ be the space of rectangular 2-tori. There is a countable dense subset $\mathcal B $ of $\mathcal A $ such that every torus in $\mathcal B$ can be minimally immersed into $ S ^ 3 $. \end{enumerate} The main content of this manuscript lies in finding minimal immersions that satisfy {\bf periodicity conditions} and hence obtaining maps of tori, rather than simply immersions of the plane. We make use of a correspondence, established by Hitchin, between minimal tori in $S^3$ and algebraic curve data. | |
| dc.description | To appear, Pacific Journal of mathematics. 27 pages, 7 figures. Minor changes only | |
| dc.identifier | https://arxiv.org/abs/math/0407304 | |
| dc.identifier | http://arxiv.org/abs/math/0407304 | |
| dc.identifier | Pacific Journal of mathematics, Nov 2007, vol 233, no 1, pp41-70 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/161181 | |
| dc.subject | Differential Geometry | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 14H70;37K25;53C42 | |
| dc.title | Minimal Tori in $S^3$ | |
| dc.type | text |