A generalization of almost Schur lemma on CR manifolds
  In this paper, we study a general almost Schur Lemma on pseudo-Hermitian (2n+1)-manifolds $(M,J,\theta)$ for $n\geq2$. When the equality of almost Schur inequality holds, we derive the contact form $\theta$ is pseudo-Einstein and the pseudo-Hermitian scalar curvature is constant. 
Jui-Tang Chen, Nguyen Thac Dung, Chin-Tung Wu
math.DG