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 

机构地区：[1]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 [2]Yau Mathematical Sciences Center, Tsinghua University, Beijing 100084, P. R. China [3]School of Mathematics and Statistics, Xinyang Normal University, Xinyang 464000, P. R. China [4]Department of Mathematics, National Tsing Hua University, Hsinchu 30013, Taiwan, China

出　　处：《Acta Mathematica Sinica,English Series》2018年第8期1313-1344,共32页数学学报（英文版）

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)

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.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.

关 键 词：CR Poisson equation CR Poincare-Lelong equation CR Yamabe solitons 

分 类 号：O186.1[理学—数学]