English

Boundary value problems in dimensions seven, four and three related to exceptional holonomy

Differential Geometry 2017-08-08 v1

Abstract

In the paper we introduce a boundary value problem for a G_{2} structure on a 7-manifold with boundary, with prescribed 3-form on the boundary. We make some general observations about this problem and then study in more detail reductions to 4 and 3 dimensions by imposing symmetry. The 3-dimensional reduction admits a dual variational formulation in terms of solutions of the real Monge-Ampere equation

Keywords

Cite

@article{arxiv.1708.01649,
  title  = {Boundary value problems in dimensions seven, four and three related to exceptional holonomy},
  author = {Simon Donaldson},
  journal= {arXiv preprint arXiv:1708.01649},
  year   = {2017}
}
R2 v1 2026-06-22T21:07:23.427Z