On the CR Poincaré–Lelong Equation, Yamabe Steady Solitons and Structures of Complete Noncompact Sasakian Manifolds

作     者：Der Chen CHANG Shu Cheng CHANG Ying Bo HAN Chien LIN 

作者机构：Department of Mathematics and Statistics Georgetown University Washington D. C. 20057 USA Graduate Institute of Applied Science and Engineering Fu Jen Catholic University Taipei 242 Taiwan China Yau Mathematical Sciences Center Tsinghua University Beijing 100084 P. R. China School of Mathematics and Statistics Xinyang Normal University Xinyang 464000 P. R. China Department of Mathematics National Tsing Hua University Hsinchu 30013 Taiwan China 

出 版 物：《Acta Mathematica Sinica,English Series》 (数学学报（英文版）)

年 卷 期：2018年第34卷第8期

页      面：1313-1344页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：partially supported by an NSF(Grant No.DMS-1408839) a McDevitt Endowment Fund at Georgetown University partially supported in part by the MOST of Taiwan partially supported by an NSFC(Grant No.11201400) Nanhu Scholars Program for Young Scholars of Xinyang Normal University the Universities Young Teachers Program of Henan Province(Grant No.2016GGJS-096) 

主　　题：CR Poisson equation CR Poincare-Lelong equation CR Yamabe solitons 

摘      要：In this paper, we solve the so-called CR Poincare-Lelong equation by solving the CR Poisson equation on a complete noncompact CR （2n ＋ 1）-manifold with nonegative pseudohermitian bisectional curvature tensors and vanishing torsion which is an odd dimensional counterpart of Kahler geometry. With applications of this solution plus the CR Liouvelle property, we study the structures of complete noncompact Sasakian manifolds and CR Yamabe steady solitons.