An Obata type result for the first eigenvalue of t

Authors: Stefan Ivanov Dimiter Vassilev

Publish Date: 2013/01/19

Volume: 103, Issue: 3, Pages: 475-504

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Abstract

We prove a CR version of the Obata’s result for the first eigenvalue of the subLaplacian in the setting of a compact strictly pseudoconvex pseudohermitian manifold which satisfies a Lichnerowicz type condition and has a divergence free pseudohermitian torsion We show that if the first positive eigenvalue of the subLaplacian takes the smallest possible value then up to a homothety of the pseudohermitian structure the manifold is the standard Sasakian unit sphere We also give a version of this theorem using the existence of a function with traceless horizontal Hessian on a complete with respect to Webster’s metric pseudohermitian manifold

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