## Kyoto Journal of Mathematics

### 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 $n\geq2$. 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.

#### Article information

Source
Kyoto J. Math., Volume 52, Number 1 (2012), 89-98.

Dates
First available in Project Euclid: 19 February 2012

https://projecteuclid.org/euclid.kjm/1329684743

Digital Object Identifier
doi:10.1215/21562261-1503763

Mathematical Reviews number (MathSciNet)
MR2892768

Zentralblatt MATH identifier
1238.32025

#### Citation

Chen, Jui-Tang; Saotome, Takanari; Wu, Chin-Tung. The CR almost Schur lemma and Lee conjecture. Kyoto J. Math. 52 (2012), no. 1, 89--98. doi:10.1215/21562261-1503763. https://projecteuclid.org/euclid.kjm/1329684743

#### References

• [CC] S.-C. Chang and H.-L. Chiu, Nonnegativity of CR Paneitz operator and its application to the CR Obata’s theorem, J. Geom. Analysis 19 (2009), 261–287.
• [DT] S. Dragomir and G. Tomassini, Differential Geometry and Analysis on CR Manifolds, Progr. Math. 246, Birkhäuser, Boston, 2006.
• [GW] Y. Ge and G. Wang, An almost Schur theorem on 4-dimensional manifolds, preprint, to appear in Proc. Amer. Math. Soc.
• [Le] J. M. Lee, Pseudo-Einstein structures on CR manifolds, Amer. J. Math. 110 (1988), 157–178.