Journal of Differential Geometry

An Obata-type theorem in CR geometry

Song-Ying Li and Xiaodong Wang

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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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J. Differential Geom., Volume 95, Number 3 (2013), 483-502.

First available in Project Euclid: 16 October 2013

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Li, Song-Ying; Wang, Xiaodong. An Obata-type theorem in CR geometry. J. Differential Geom. 95 (2013), no. 3, 483--502. doi:10.4310/jdg/1381931736.

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