On the CR–Obata theorem and some extremal problems associated to pseudoscalar curvature on the real ellipsoids in ℂⁿ⁺¹

Li, Song-Ying; Tran, MyAn

doi:10.1090/S0002-9947-2011-05396-1

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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