Constructing Associative 3-folds by Evolution Equations
| dc.creator | Lotay, Jason | |
| dc.date | 2004-01-13 | |
| dc.date | 2006-07-04 | |
| dc.date.accessioned | 2026-07-07T06:35:54Z | |
| dc.date.available | 2026-07-07T06:35:54Z | |
| dc.description | This paper gives two methods for constructing associative 3-folds in R^7, based around the fundamental idea of evolution equations, and uses these methods to construct examples of these geometric objects. The paper is a generalisation of the work by Joyce in math.DG/0008021, math.DG/0008155, math.DG/0010036 and math.DG/0012060 on special Lagrangian 3-folds in C^3. The two methods described involve the use of an affine evolution equation with affine evolution data and the area of ruled submanifolds. We first give a derivation of an evolution equation for associative 3-folds from which we derive an affine evolution equation using affine evolution data. We then use this on an example of such data to construct a 14-dimensional family of associative 3-folds. One of the main result of the paper is then an explicit solution of the system of differential equations generated in a particular case to give a 12-dimensional family of associative 3-folds. We also find that there is a straightforward condition that ensures that the associative 3-folds constructed are closed and diffeomorphic to S^1xR^2, rather than R^3. In the final section we define ruled associative 3-folds and derive an evolution equation for them. This then allows us to characterise a family of ruled associative 3-folds using two real analytic maps that must satisfy two partial differential equations. We finish by giving a means of constructing ruled associative 3-folds M from r-oriented two-sided associative cones M_0 such that M is asymptotically conical to M_0 with order O(r^{-1}). | |
| dc.description | 43 pages, LaTeX; minor corrections, mainly typos, and slight changes in presentation, including added references | |
| dc.identifier | https://arxiv.org/abs/math/0401123 | |
| dc.identifier | http://arxiv.org/abs/math/0401123 | |
| dc.identifier | Communications in Analysis and Geometry, Volume 13, Number 5, 999-1037, 2005 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/99937 | |
| dc.subject | Differential Geometry | |
| dc.subject | 53C38 | |
| dc.title | Constructing Associative 3-folds by Evolution Equations | |
| dc.type | text |