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Irregular Eguchi–Hanson type metrics and their soliton analogues
Pure and Applied Mathematics Quarterly ( IF 0.7 ) Pub Date : 2021-01-01 , DOI: 10.4310/pamq.2021.v17.n1.a2
Akito Futaki 1
Affiliation  

We verify the extension to the zero section of momentum construction of Kähler–Einstein metrics and Kähler–Ricci solitons on the total space $Y$ of positive rational powers of the canonical line bundle of toric Fano manifolds with possibly irregular Sasaki–Einstein metrics. More precisely, we show that the extended metric along the zero section has an expression which can be extended to $Y$, restricts to the associated unit circle bundle as a transversely Kähler–Einstein (Sasakian eta‑Einstein) metric scaled in the Reeb flow direction, and that there is a Riemannian submersion from the scaled Sasakian eta‑Einstein metric to the induced metric of the zero section.

中文翻译:

不规则的Eguchi–Hanson类型指标及其孤子类似物

我们验证了在具有复曲面法诺流形的规范线束的正空间有正则幂的Kähler-Einstein度量和Kähler-Ricci孤子的动量构造零部分的扩展,其中Sasaki-Einstein度量可能是不规则的。更准确地说,我们证明了沿零部分的扩展度量具有可以扩展为$ Y $的表达式,并限制为相关的单位圆束,作为在Reeb流中缩放的横向Kähler-Einstein(Sasakian eta-Einstein)度量方向,并且存在从比例尺的Sasakian eta-Einstein度量到零部分的诱导度量的黎曼浸没。
更新日期:2021-01-01
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