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
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}
}