On the Hamilton-Tian Conjecture in a compact transverse Fano Sasakian $5$-manifold
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| Main Authors: | , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866910239913148416 |
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| author | Chang, Shu-Cheng Han, Yingbo Lin, Chien Wu, Chin-Tung |
| author_facet | Chang, Shu-Cheng Han, Yingbo Lin, Chien Wu, Chin-Tung |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_20852 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the Hamilton-Tian Conjecture in a compact transverse Fano Sasakian $5$-manifold Chang, Shu-Cheng Han, Yingbo Lin, Chien Wu, Chin-Tung Differential Geometry 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. |
| title | On the Hamilton-Tian Conjecture in a compact transverse Fano Sasakian $5$-manifold |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2605.20852 |