An Obata type result for the first eigenvalue of the sub-Laplacian on a CR manifold with a divergence free torsion

Details An Obata type result for the first eigenvalue of the sub-Laplacian on a CR manifold with a divergence free torsion An Obata type result for the first eigenvalue of the sub-Laplacian on a CR manifold with a divergence free torsion

2012-03-26

arxiv.org/abs/1203.5812v2

Mathematics

Differential Geometry

The three dimensional case is included

Scientific paper

We prove an Obata type result for the first positive eigenvalue of the sub-Laplacian on a compact strictly pseudoconvex pseudohermitian manifold with a divergence free Webster torsion. We show that if the first positive eigenvalue of the sub-Laplacian on a strictly pseudoconvex pseudohermitian manifold with a divergence free Webster torsion takes the smallest possible value then, up to a homothety of the pseudohermitian structure, the manifold is the unit sphere in complex space endowed with its standard CR pseudohermitian structure.

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