Structures in Dimension 7
نویسنده
چکیده
The conformal infinity of a quaternionic-Kähler 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-Kähler metric. On the contrary, in dimension 7, we prove a criterion for quaternionic contact structures to be the conformal infinity of a quaternionicKähler 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-Kähler metrics on the 8-ball. Finally, we construct a 25-parameter family of Sp(1)-invariant complete quaternionic-Kähler metrics on the 8-ball together with the 25-parameter family of their boundaries.
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