The Biquard connection on Riemannian quaternionic contact manifolds

Abstract

The conformal infinity of a quaternionic-Kahler metric on a $4n$ dimensional manifold with boundary is a codimension $3$-distribution on the boundary called quaternionic contact structure. In order to study such structures O.Biquard [1] has introduced a unique connection which preserves the structure and whose torsion tensor satisfies some conditions. This paper is devoted to obtaining an explicit formula for the torsion tensor and for the connection itself.