On the twistor space of a quaternionic contact manifold

In this note, we prove that the CR manifold 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.

► We study the CR-type Fefferman space associated to a quaternionic contact manifold. ► We prove that it is equivalent to the CR twistor space constructed by Biquard. ► This relates parabolic geometry methods to an underlying geometric construction. ► One application is to identify the conformal Fefferman metrics of the structures.