Nonnegativity of CR Paneitz Operator and Its Application to the CR Obata’s Theorem
Resource
Journal of Geometric Analysis 19 (2): 261-287
Journal
Journal of Geometric Analysis
Journal Volume
19
Journal Issue
2
Pages
261-287
Date Issued
2009
Date
2009
Author(s)
Chiu, Hung-Lin
Abstract
In this paper, we first prove the CR analogue of M. Obata's theorem on a closed pseudohermitian (2n+1)-manifold with free pseudohermitian torsion. Secondly, we have the CR analogue of Li-Yau's eigenvalue estimate on the lower bound estimate of positive first eigenvalue of the sub-Laplacian on a closed pseudohermitian (2n+1)-manifold with a more general curvature condition for n≥2. The key step is a discovery of CR analogue of Bochner formula which involving the CR Paneitz operator and nonnegativity of CR Paneitz operator P 0 for n≥2. © 2009 Mathematica Josephina, Inc.
Type
journal article
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