The twistor space of a quaternionic contact manifold

TL;DR

This paper characterizes when the CR structure on the twistor space of a quaternionic contact manifold is normal, linking it to the commutation of Ricci curvature with quaternionic endomorphisms.

Contribution

It provides a necessary and sufficient condition for the normality of the CR structure on the twistor space based on Ricci curvature properties.

Findings

Normality of CR structure is equivalent to Ricci curvature commuting with quaternionic endomorphisms.

Establishes a precise geometric criterion for twistor space structures.

Connects curvature conditions with complex geometric structures in quaternionic contact manifolds.

Abstract

We show that the CR structure on the twistor space of a quaternionic contact structure described by Biquard is normal if and only if the Ricci curvature of the Biquard connection commutes with the endomorphisms in the quaternionic structure of the contact distribution.