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AN OBATA-TYPE THEOREM ON A THREE-DIMENSIONAL CR MANIFOLD

Published online by Cambridge University Press:  13 August 2013

S. IVANOV  and
D. VASSILEV
S. IVANOV
Affiliation:
Faculty of Mathematics and Informatics, University of Sofia, blvd. James Bourchier 5, Sofia 1164, Bulgaria e-mail: ivanovsp@fmi.uni-sofia.bg
D. VASSILEV
Affiliation:
Department of Mathematics and Statistics, University of New Mexico, Albuquerque, NM 87131-0001, USA e-mail: vassilev@math.unm.edu
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Abstract

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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.

Keywords

53C2653C2558J6032V0532V2053C56
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 56 , Issue 2 , May 2014 , pp. 283 - 294
Copyright
Copyright © Glasgow Mathematical Journal Trust 2013 

References

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