Abstract
A closed CR 3-manifold is said to have \(C_{0}\)-positive pseudohermitian curvature if \((W+C_{0}Tor)(X,X)>0\) for any \(0\ne X\in T_{1,0}(M)\). We discover an obstruction for a closed CR 3-manifold to possess \(C_{0}\) -positive pseudohermitian curvature. We classify closed three-dimensional CR Yamabe solitons according to \(C_{0}\)-positivity for \(C_{0}=1\) and the potential function lies in the kernel of Paneitz operator. Moreover, we show that any closed three-dimensional CR torsion soliton must be the standard Sasakian space form. At last, we discuss the persistence of \(C_{0}\)-positivity along the CR torsion flow starting from a pseudo-Einstein contact form.
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25 February 2020
In the original article, the equation 2.4 was incorrectly published.
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Acknowledgements
Part of the project was done during the visit of the second author to Yau Mathematical Sciences Center, Tsinghua University. He would like to express his thanks for the warm hospitality.
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Huai-Dong Cao: Research supported in part by a grant from the Simons Foundation (#586694 HC).
Shu-Cheng Chang and Chih-Wei Chen: Research supported in part by the MOST of Taiwan.
The original version of this article was revised: The equation 2.4 has been corrected in the original article.
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Cao, HD., Chang, SC. & Chen, CW. \(C_0\)-positivity and a classification of closed three-dimensional CR torsion solitons. Math. Z. 296, 1065–1080 (2020). https://doi.org/10.1007/s00209-020-02471-2
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DOI: https://doi.org/10.1007/s00209-020-02471-2