On quaternionic contact Fefferman spaces

Abstract

We investigate the Fefferman spaces of conformal type which are induced, via parabolic geometry, by the quaternionic contact (qc) manifolds introduced by O. Biquard. Equivalent characterizations of these spaces are proved: as conformal manifolds with symplectic conformal holonomy of the appropriate signature; as pseudo-Riemannian manifolds admitting conformal Killing fields satisfying a conformally invariant system of conditions analogous to G. Sparling's criteria for CR Fefferman spaces; and as the total space of a SO ( 3 ) - or S 3 -bundle over a qc manifold with the conformally equivalent metrics defined directly by Biquard. Global as well as local results are acquired.