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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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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 $A_j \in (-1,1).$
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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