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

In this paper, we solve the so-called CR Poincaré–Lelong equation by solving the CR Poisson equation on a complete noncompact CR (2 n + 1)-manifold with nonegative pseudohermitian bisectional curvature tensors and vanishing torsion which is an odd dimensional counterpart of Kähler geometry. With app...

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Bibliographic Details
Published in:Acta mathematica Sinica. English series 2018-08, Vol.34 (8), p.1313-1344
Main Authors: Chang, Der Chen, Chang, Shu Cheng, Han, Ying Bo, Lin, Chien
Format: Article
Language:English
Subjects:
Curvature
Manifolds (mathematics)
Mathematical analysis
Mathematics
Mathematics and Statistics
Poisson equation
Solitary waves
Tensors
Topological manifolds
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Summary:In this paper, we solve the so-called CR Poincaré–Lelong equation by solving the CR Poisson equation on a complete noncompact CR (2 n + 1)-manifold with nonegative pseudohermitian bisectional curvature tensors and vanishing torsion which is an odd dimensional counterpart of Kähler 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.
ISSN:1439-8516
1439-7617
DOI:10.1007/s10114-018-7342-0