The almost Schur Lemma in quaternionic contact geometry

We establish quaternionic contact (qc) versions of the so called Almost Schur Lemma, which give estimations of the qc scalar curvature on a compact qc manifold to be a constant in terms of the norm of the [-1] -component and the norm of the trace-free part of the [3]-component of the horizontal qc Ricci tensor and the torsion endomorphism, under certain positivity conditions.