On the CR analogue of Obata's theorem in a pseudohermitian 3-manifold
Journal
Mathematische Annalen
Journal Volume
345
Journal Issue
1
Pages
33-51
Date Issued
2009
Author(s)
Chiu, Hung-Lin
Abstract
In this paper, we first prove the CR analogue of Obata's theorem on a closed pseudohermitian 3-manifold with zero pseudohermitian torsion. Secondly, instead of zero torsion, we have the CR analogue of Li-Yau's eigenvalue estimate on the lower bound estimate of positive first eigenvalue of the sub-Laplacian in a closed pseudohermitian 3-manifold with nonnegative CR Paneitz operator P0. Finally, we have a criterion for the positivity of first eigenvalue of the sub-Laplacian on a complete noncompact pseudohermitian 3-manifold with nonnegative CR Paneitz operator. The key step is a discovery of integral CR analogue of Bochner formula which involving the CR Paneitz operator. © Springer-Verlag 2009.
Type
journal article