The CR almost Schur lemma and Lee conjecture

Abstract

In this paper, we first derive the CR analogue of the almost Schur lemma on a pseudo-Hermitian $(2n+1)$-manifold $(M,J,\theta )$ for $n\ge 2$. Second, we study a sufficient condition for the existence of a pseudo-Einstein contact form when the CR structure of $M$ has vanishing first Chern class which is related to the J. M. Lee conjecture.