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arXiv · 1208.1040

An Obata-type theorem on a three-dimensional CR manifold

Stefan Ivanov·Dimiter Vassilev
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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.

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Stefan Ivanov, Dimiter Vassilev. 2012-08-30. An Obata-type theorem on a three-dimensional CR manifold. https://arxiv.org/abs/1208.1040

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