Associative submanifolds and gradient cycles. (English) Zbl 07817743
Cao, Huai-Dong (ed.) et al., Differential geometry, Calabi-Yau theory, and general relativity. Part 2. Lectures and articles celebrating the 70th birthday of Shing-Tung Yau, Harvard University, Cambridge, MA, USA, May 2019. Somerville, MA: International Press. Surv. Differ. Geom. 24, 39-65 (2022).
This paper discusses a model for associative submanifolds in \(G_2\)-manifolds with \(K3\) fibrations in the adiabatic limit. The model involves graphs in a \(3\)-manifold whose edges are locally gradient flow lines. The authors prove that this model produces analogues of known singularity formation phenomena for associative submanifolds. They also propose conjectures on the existence of associative and special Lagrangian submanifolds in certain product spaces, corresponding to the vertices of the graphs.
For the entire collection see [Zbl 1492.53003].
For the entire collection see [Zbl 1492.53003].
Reviewer: Yuwei Fan (Beijing)
MSC:
| 53C40 | Global submanifolds |
| 53C29 | Issues of holonomy in differential geometry |
| 53C10 | \(G\)-structures |
| 53D12 | Lagrangian submanifolds; Maslov index |
