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arXiv · 2203.00374

Convergence of the Sasaki-Ricci flow on Sasakian 5-manifolds of general type

Shu-Cheng Chang·Yingbo Han·Chien Lin·Chin-Tung Wu
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Abstract

In this paper, we show that the uniform L^{4}-bound of the transverse Ricci curvature along the Sasaki-Ricci flow on a compact quasi-regular Sasakian (2n+1)-manifold M of general type. As an application, any solution of the normalized Sasaki-Ricci flow converges in the Cheeger-Gromov sense to the unique singular Sasaki {\eta}-Einstein metric on the transverse canonical model M_{can} of M if n is less than or equal to 3. In particular for n equal to 2, M_{can} is a S^{1}-orbibundle over the unique Keahler-Einstein orbifold surface (Z_{can},{\omega}_{KE}) with finite point orbifold singularities. The floating foliation (-2)-curves in M will be contracted to orbifold points by the Sasaki-Ricci flow as t goes to infinite.

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Shu-Cheng Chang, Yingbo Han, Chien Lin, Chin-Tung Wu. 2022-03-01. Convergence of the Sasaki-Ricci flow on Sasakian 5-manifolds of general type. https://arxiv.org/abs/2203.00374

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