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arXiv · 2605.20852

On the Hamilton-Tian Conjecture in a compact transverse Fano Sasakian $5$-manifold

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

In this paper, we first confirm the Hamilton-Tian conjecture for the Sasaki-Ricci flow in a compact transverse Fano quasi-regular Sasakian $5$-manifold with klt foliation singularities. Secondly, we derive the compactness theorem of Sasaki-Ricci solitons on transverse Fano quasi-regular Sasakian $5$-manifolds. Then,by the second Sasakian structure theorem, we confirm the Hamilton-Tian conjecture for a compact transverse Fano Sasakian $5$-manifold. With its applications, we show that the gradient Sasaki-Ricci soliton orbifold metric on a compact Sasakian $5$-manifold is Sasaki-Einstein if $M$ is transverse $K$-stable.

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Shu-Cheng Chang, Yingbo Han, Chien Lin, Chin-Tung Wu. 2026-05-20. On the Hamilton-Tian Conjecture in a compact transverse Fano Sasakian $5$-manifold. https://arxiv.org/abs/2605.20852

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