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Transactions of the American Mathematical Society
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
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)=\vert z\vert^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
Email: sli@math.uci.edu

MyAn Tran
Affiliation: Department of Mathematics, University of California, Irvine, California 92697–3875
Email: mtran@math.uci.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-2011-05396-1
PII: S 0002-9947(2011)05396-1
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.