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arXiv · 1804.03526

On the CR Poincar\'e-Lelong equation, Yamabe steady solitons and structures of complete noncompact Sasakian manifolds

Der-Chen Chang·Shu-Cheng Chang·Yingbo Han·Chien Lin
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Abstract

In this paper, we solve the so-called CR Poincar\'e-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 K\"ahler 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.

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Der-Chen Chang, Shu-Cheng Chang, Yingbo Han, Chien Lin. 2018-04-08. On the CR Poincar\'e-Lelong equation, Yamabe steady solitons and structures of complete noncompact Sasakian manifolds. https://arxiv.org/abs/1804.03526

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