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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

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


Authors: Song-Ying Li and MyAn Tran
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
Published electronically: March 22, 2011
MathSciNet review: 2792978
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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 $A_j \in (-1,1).$


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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
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.