Geodesic
AN OBATA-TYPE THEOREM ON A THREE-DIMENSIONAL CR MANIFOLD
Glasgow mathematical journal, Tome 56 (2014) no. 2, pp. 283-294

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DOI

We prove the CR version of the Obata's result for the first eigenvalue of the sub-Laplacian in the setting of a compact strictly pseudoconvex pseudohermitian three-dimensional manifold with non-negative CR-Paneitz operator which satisfies a Lichnerowicz-type condition. We show that if the first positive eigenvalue of the sub-Laplacian takes the smallest possible value, then, up to a homothety of the pseudohermitian structure, the manifold is the standard Sasakian three-dimensional unit sphere.
DOI : 10.1017/S0017089513000256
Mots-clés : 53C26, 53C25, 58J60, 32V05, 32V20, 53C56 
IVANOV, S.; VASSILEV, D. AN OBATA-TYPE THEOREM ON A THREE-DIMENSIONAL CR MANIFOLD. Glasgow mathematical journal, Tome 56 (2014) no. 2, pp. 283-294. doi: 10.1017/S0017089513000256
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     title = {AN {OBATA-TYPE} {THEOREM} {ON} {A} {THREE-DIMENSIONAL} {CR} {MANIFOLD}},
     journal = {Glasgow mathematical journal},
     pages = {283--294},
     year = {2014},
     volume = {56},
     number = {2},
     doi = {10.1017/S0017089513000256},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089513000256/}
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