On the CR analogue of Obata's theorem in a pseudohermitian 3-manifold

Please use this identifier to cite or link to this item: http://ir.lib.ncu.edu.tw/handle/987654321/27957

Title:	On the CR analogue of Obata's theorem in a pseudohermitian 3-manifold
Authors:	Chang,SC;Chiu,HL
Contributors:	數學研究所
Keywords:	1ST EIGENVALUE;SUB-LAPLACIAN;MANIFOLDS;SUBLAPLACIAN;CURVATURE
Date:	2009
Issue Date:	2010-06-29 19:38:52 (UTC+8)
Publisher:	中央大學
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 P (0). 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.
Relation:	MATHEMATISCHE ANNALEN
Appears in Collections:	[Graduate Institute of Mathematics] journal & Dissertation

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