On the twistor space of a quaternionic contact manifold

TL;DR

This paper demonstrates that the CR manifold derived from the canonical parabolic geometry of a quaternionic contact manifold via a Fefferman-type construction is equivalent to Biquard's CR twistor space, linking two geometric frameworks.

Contribution

It establishes the equivalence between the CR manifold from parabolic geometry and Biquard's CR twistor space for qc manifolds, unifying different geometric approaches.

Findings

Proves the CR manifold from parabolic geometry matches Biquard's twistor space.

Links two different geometric constructions of quaternionic contact manifolds.

Provides a new perspective on the structure of qc manifolds.

Abstract

In this note, we prove that the CR manifold which is induced from the canonical parabolic geometry of a quaternionic contact (qc) manifold via a Fefferman-type construction is equivalent to the CR twistor space of the qc manifold defined by O. Biquard.