On quaternionic contact Fefferman spaces

TL;DR

This paper explores the geometric structures of quaternionic contact Fefferman spaces, establishing their characterizations through conformal holonomy, Killing fields, and bundle constructions, with both local and global insights.

Contribution

It provides new characterizations of quaternionic contact Fefferman spaces via conformal holonomy, Killing fields, and bundle descriptions, advancing understanding of their geometric properties.

Findings

Characterization as conformal manifolds with symplectic holonomy

Identification of conformal Killing fields satisfying invariant conditions

Description as SO(3)- or S^3-bundles over qc manifolds

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 analog to G. Sparling's criteria; 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.