obata operators

Kazushige Obata, Kaori Mukai, Yusuke Tsujimura, Kenji Ishiwata, Yohei Kawano, Yoshiyuki Minegishi, Naohiro Watanabe, and Hajime Karasuyama Department of Immune Regulation, Tokyo Medical and Dental University Graduate School, 1-5-45 Yushima, Bunkyo-ku, Tokyo 113-8519, Japan, Department of Tropical Medicine, The Jikei University School of Medicine, 3-25-8 Nishishinbashi, Minato-ku, Tokyo 105-8461...

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An Obata-type Theorem in Cr Geometry

2012

SONG-YING LI XIAODONG WANG

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 which characterizes the CR sphere in terms of a nonzero funct...

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