Classification of gradient Einstein-type Kähler manifolds with $α=0$
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866915213129809920 |
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| author | Maeta, Shun |
| author_facet | Maeta, Shun |
| contents | Thanks to the ambitious project initiated by Catino, Mastrolia, Monticelli and Rigoli, which aims to provide a unified viewpoint for various geometric solitons, many classes, including Ricci solitons, Yamabe solitons, $k$-Yamabe solitons, quasi-Yamabe solitons, and conformal solitons, can now be studied under a unified framework known as Einstein-type manifolds. Einstein-type manifolds are characterized by four constants, denoted by $α, β, μ$ and $ρ$. In this paper, we completely classify all non-trivial, complete gradient Einstein-type Kähler manifolds with $α= 0$. As a corollary, rotational symmetry for many classes is obtained. In particular, we show that any non-trivial complete gradient quasi-Yamabe soliton on Kähler manifolds is rotationally symmetric. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_19596 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Classification of gradient Einstein-type Kähler manifolds with $α=0$ Maeta, Shun Differential Geometry 53C25, 53C55, 53C21, 32Q15, 53C20 Thanks to the ambitious project initiated by Catino, Mastrolia, Monticelli and Rigoli, which aims to provide a unified viewpoint for various geometric solitons, many classes, including Ricci solitons, Yamabe solitons, $k$-Yamabe solitons, quasi-Yamabe solitons, and conformal solitons, can now be studied under a unified framework known as Einstein-type manifolds. Einstein-type manifolds are characterized by four constants, denoted by $α, β, μ$ and $ρ$. In this paper, we completely classify all non-trivial, complete gradient Einstein-type Kähler manifolds with $α= 0$. As a corollary, rotational symmetry for many classes is obtained. In particular, we show that any non-trivial complete gradient quasi-Yamabe soliton on Kähler manifolds is rotationally symmetric. |
| title | Classification of gradient Einstein-type Kähler manifolds with $α=0$ |
| topic | Differential Geometry 53C25, 53C55, 53C21, 32Q15, 53C20 |
| url | https://arxiv.org/abs/2503.19596 |