Open Access
November 2013 An Obata-type theorem in CR geometry
Song-Ying Li, Xiaodong Wang
J. Differential Geom. 95(3): 483-502 (November 2013). DOI: 10.4310/jdg/1381931736


We discuss a sharp lower bound for the first positive eigenvalue of the sublaplacian on a closed, strictly pseudoconvex pseudohermitian manifold of dimension $2m + 1 \geq 5$. We prove that the equality holds iff the manifold is equivalent to the CR sphere up to a scaling. For this purpose, we establish an Obata-type theorem in CR geometry that characterizes the CR sphere in terms of a nonzero function satisfying a certain overdetermined system. Similar results are proved in dimension 3 under an additional condition.


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Song-Ying Li. Xiaodong Wang. "An Obata-type theorem in CR geometry." J. Differential Geom. 95 (3) 483 - 502, November 2013.


Published: November 2013
First available in Project Euclid: 16 October 2013

zbMATH: 1277.32038
MathSciNet: MR3128992
Digital Object Identifier: 10.4310/jdg/1381931736

Rights: Copyright © 2013 Lehigh University

Vol.95 • No. 3 • November 2013
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