Quaternionic contact structures in dimension 7
Abstract
The conformal infinity of a quaternionic-Kahler metric on a 4n-manifold with boundary is a codimension 3-distribution on the boundary called quaternionic contact. In dimensions 4n-1 greater than 7, a quaternionic contact structure is always the conformal infinity of a quaternionic-Kahler metric. On the contrary, in dimension 7, we prove a criterion for quaternionic contact structures to be the conformal infinity of a quaternionic- Kahler metric. This allows us to find the quaternionic-contact structures on the 7-sphere close to the conformal infinity of the quaternionic hyperbolic metric and which are the boundaries of complete quaternionic-Kahler metrics on the 8-ball. Finally, we construct a 25-parameter family of Sp(1)-invariant complete quaternionic-Kahler metrics on the 8-ball together with the 25-parameter family of their boundaries.
Keywords
Cite
@article{arxiv.math/0311436,
title = {Quaternionic contact structures in dimension 7},
author = {David Duchemin},
journal= {arXiv preprint arXiv:math/0311436},
year = {2007}
}