Quaternionic contact structures in dimension 7

Details Quaternionic contact structures in dimension 7 Quaternionic contact structures in dimension 7

2003-11-25

arxiv.org/abs/math/0311436v1

Mathematics

Differential Geometry

Scientific paper

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.

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