An Obata-type theorem on a three-dimensional CR manifold
Differential Geometry
2012-08-31 v3 Analysis of PDEs
Abstract
We prove a 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-Panietz 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
Cite
@article{arxiv.1208.1040,
title = {An Obata-type theorem on a three-dimensional CR manifold},
author = {Stefan Ivanov and Dimiter Vassilev},
journal= {arXiv preprint arXiv:1208.1040},
year = {2012}
}
Comments
Improved exposition and remarks on references and citations. arXiv admin note: substantial text overlap with arXiv:1203.5812