Minimal tori with low nullity
| dc.creator | Johnson, David L. | |
| dc.creator | Perdomo, Oscar | |
| dc.date | 2007-11-12 | |
| dc.date.accessioned | 2026-07-07T08:42:19Z | |
| dc.date.available | 2026-07-07T08:42:19Z | |
| dc.description | The nullity of a minimal submanifold $M\subset S^{n}$ is the dimension of the nullspace of the second variation of the area functional. That space contains as a subspace the effect of the group of rigid motions $SO(n+1)$ of the ambient space, modulo those motions which preserve $M$, whose dimension is the Killing nullity $kn(M)$ of $M$. In the case of 2-dimensional tori $M$ in $S^{3}$, there is an additional naturally-defined 2-dimensional subspace; the dimension of the sum of the action of the rigid motions and this space is the natural nullity $nnt(M)$. In this paper we will study minimal tori in $S^{3}$ with natural nullity less than 8. We construct minimal immersions of the plane $R^{2}$ in $S^{3}$ that contain all possible examples of tori with $nnt(M)<8$. We prove that the examples of Lawson and Hsiang with $kn(M)=5$ also have $nnt(M)=5$, and we prove that if the $nnt(M)\le6$ then the group of isometries of $M$ is not trivial. | |
| dc.description | 24 pages, no figures | |
| dc.identifier | https://arxiv.org/abs/0711.1712 | |
| dc.identifier | http://arxiv.org/abs/0711.1712 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/141922 | |
| dc.subject | Differential Geometry | |
| dc.subject | 58E12, 58E20, 53C42, 53C43 | |
| dc.title | Minimal tori with low nullity | |
| dc.type | text |