## On the CR–Obata theorem and some extremal problems associated to pseudoscalar curvature on the real ellipsoids in $\mathbb {C}^{n+1}$

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- by Song-Ying Li and MyAn Tran PDF
- Trans. Amer. Math. Soc.
**363**(2011), 4027-4042 Request permission

## Abstract:

This paper studies the CR-version of Obata theorem on a pseudo-Hermitian CR-manifold $(M,\theta )$. The main result of the paper is proving that CR–Obata theorem holds on real ellipsoid $E(A)$ with contact form $\theta =\frac {1}{2i} (\partial \rho _A - \bar {\partial } \rho _A)$, where $\rho _A(z)=|z|^2 + \mathrm {Re} \sum ^n_{j=1}A_jz^2_j-1$ with $A_j \in (-1,1).$## References

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## Additional Information

**Song-Ying Li**- Affiliation: Department of Mathematics, University of California, Irvine, California 92697–3875
- MR Author ID: 228844
- Email: sli@math.uci.edu
**MyAn Tran**- Affiliation: Department of Mathematics, University of California, Irvine, California 92697–3875
- Email: mtran@math.uci.edu
- Received by editor(s): April 1, 2009
- Published electronically: March 22, 2011
- © Copyright 2011
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc.
**363**(2011), 4027-4042 - MSC (2010): Primary 32V05, 32V20; Secondary 53C56
- DOI: https://doi.org/10.1090/S0002-9947-2011-05396-1
- MathSciNet review: 2792978