Connected sums of special Lagrangian submanifolds
| dc.creator | Lee, Dan A. | |
| dc.date | 2003-03-18 | |
| dc.date.accessioned | 2026-07-07T04:56:10Z | |
| dc.date.available | 2026-07-07T04:56:10Z | |
| dc.description | Let $M_1$ and $M_2$ be special Lagrangian submanifolds of a compact Calabi-Yau manifold $X$ that intersect transversely at a single point. We can then think of $M_1\cup M_2$ as a singular special Lagrangian submanifold of $X$ with a single isolated singularity. We investigate when we can regularize $M_1\cup M_2$ in the following sense: There exists a family of Calabi-Yau structures $X_α$ on $X$ and a family of special Lagrangian submanifolds $M_α$ of $X_α$ such that $M_α$ converges to $M_1\cup M_2$ and $X_α$ converges to the original Calabi-Yau structure on $X$. We prove that a regularization exists in two key cases: (1) when the complex dimension of $X$ is three, $\Hol(X)=\SU(3)$, and $[M_1]$ is not a multiple of $[M_2]$ in $H_3(X)$, and (2) when $X$ is a torus with complex dimension at least three, $M_1$ is flat, and the intersection of $M_1$ and $M_2$ satisfies a certain angle criterion. One can easily construct examples of the second case, and thus as a corollary we construct new examples of non-flat special Lagrangian submanifolds of Calabi-Yau tori. | |
| dc.description | 23 pages | |
| dc.identifier | https://arxiv.org/abs/math/0303224 | |
| dc.identifier | http://arxiv.org/abs/math/0303224 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/66826 | |
| dc.subject | Differential Geometry | |
| dc.subject | 53C | |
| dc.title | Connected sums of special Lagrangian submanifolds | |
| dc.type | text |