Connected sums of special Lagrangian submanifolds

Details Connected sums of special Lagrangian submanifolds Connected sums of special Lagrangian submanifolds

2003-03-18

arxiv.org/abs/math/0303224v1

Mathematics

Differential Geometry

23 pages

Scientific paper

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 $X_\alpha$ on $X$ and a family of special Lagrangian submanifolds $M_\alpha$ of $X_\alpha$ such that $M_\alpha$ converges to $M_1\cup M_2$ and $X_\alpha$ 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.

Affiliated with

Also associated with

No associations

Rating

Connected sums of special Lagrangian submanifolds does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Connected sums of special Lagrangian submanifolds, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Connected sums of special Lagrangian submanifolds will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-118732