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.
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)
