An obata-type theorem in cr geometry

Song-Ying Li Department of Mathematics University of California Xiaodong Wang Michigan State University

Differential Geometry mathscidoc:1609.10339

Journal of Differential Geometry, 95, (3), 483-502, 2013
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 ≥ 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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@inproceedings{song-ying2013an,
  title={AN OBATA-TYPE THEOREM IN CR GEOMETRY},
  author={Song-Ying Li, and Xiaodong Wang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160914083703062902001},
  booktitle={Journal of Differential Geometry},
  volume={95},
  number={3},
  pages={483-502},
  year={2013},
}
Song-Ying Li, and Xiaodong Wang. AN OBATA-TYPE THEOREM IN CR GEOMETRY. 2013. Vol. 95. In Journal of Differential Geometry. pp.483-502. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160914083703062902001.
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