[geometry-ml:06836] 名古屋大学幾何学セミナー

[kasuya ＠ math.nagoya-u.ac.jp]

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名古屋大学の糟谷久矢です。
名古屋大学の幾何学セミナーの予定
https://www.math.nagoya-u.ac.jp/ja/research/calendar/data/1778653041-84.html
を以下にお知らせします。
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糟谷

2026/6/2、16:30～18:00、理学部A館　328セミナー室
講演者：中村 聡 (名古屋工業大学)
タイトル：Soliton type metrics associated with weighted CSCK metrics on Fano 
manifolds
要旨
We study weighted constant scalar curvature Kähler ((v,w)-CSCK) metrics, 
introduced by Lahdili, and their relationship with soliton type 
(g-soliton) metrics on Fano manifolds.The (v,w)-CSCK metrics provide a 
unified framework encompassing several canonical metrics, including 
constant scalar curvature Kähler metrics, extremal metrics, and constant 
scalar curvature Sasaki metrics.The g-solitons provide a unified 
framework including Kähler-Einstein metrics, Mabuchi soliton, 
Kähler-Ricci soliton, and Sasaki-Einstein metrics. We introduce a 
natural weight function  associated with a pair of weights (v,w), and 
prove that, under suitable assumptions, the existence of a (v,w)-CSCK 
metric in the first Chern class is equivalent to the existence of a 
corresponding -soliton. This result extends earlier equivalences between 
the existence of extremal metrics and that of Mabuchi solitons, and 
shows that the existence problem for weighted CSCK metrics on Fano 
manifolds can be reduced to solving a complex Monge?Ampère equation 
associated with a soliton-type metric.