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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

The diameter estimate and its application to CR Obata's Theorem on closed pseudohermitian $ (2n+1)$-manifolds


Authors: Shu-Cheng Chang and Chin-Tung Wu
Journal: Trans. Amer. Math. Soc. 364 (2012), 3349-3363
MSC (2010): Primary 32V05, 32V20; Secondary 53C56
Published electronically: March 7, 2012
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Abstract: In this paper, we obtain a sharp lower bound estimate for diameters with respect to an adapted metric in closed pseudohermitian $ (2n+1)$-manifolds when a sharp lower bound estimate for the first positive eigenvalue of the sublaplacian is achieved. As a consequence, we confirm the CR Obata Conjecture on a closed pseudohermitian $ (2n+1)$-manifold with an extra condition on covariant derivatives of torsion.


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Additional Information

Shu-Cheng Chang
Affiliation: Department of Mathematics, National Taiwan University, Taipei 10617, Taiwan, Republic of China – and – Taida Institute for Mathematical Sciences (TIMS), National Taiwan University, Taipei 10617, Taiwan, Republic of China
Email: scchang@math.ntu.edu.tw

Chin-Tung Wu
Affiliation: Department of Applied Mathematics, National PingTung University of Education, PingTung, Taiwan 90003, Republic of China
Email: ctwu@mail.npue.edu.tw

DOI: http://dx.doi.org/10.1090/S0002-9947-2012-05620-0
PII: S 0002-9947(2012)05620-0
Keywords: Lichnerowicz-Obata Theorem, sublaplacian, CR Paneitz operator, pseudohermitian manifold, pseudohermitian Ricci curvature, pseudohermitian torsion.
Received by editor(s): February 3, 2010
Published electronically: March 7, 2012
Additional Notes: This research was supported in part by NSC
Article copyright: © Copyright 2012 American Mathematical Society