Mabuchi Kähler solitons versus extremal Kähler metrics and beyond

Using the Yau–Tian–Donaldson type correspondence for ‐solitons established by Han–Li, we show that a smooth complex ‐dimensional Fano variety admits a Mabuchi soliton provided it admits an extremal Kähler metric whose scalar curvature is strictly less than . Combined with previous observations by Ma...

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Bibliographic Details
Published in:The Bulletin of the London Mathematical Society 2024-12
Main Authors: Apostolov, Vestislav, Lahdili, Abdellah, Nitta, Yasufumi
Format: Article
Language:English
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Summary:Using the Yau–Tian–Donaldson type correspondence for ‐solitons established by Han–Li, we show that a smooth complex ‐dimensional Fano variety admits a Mabuchi soliton provided it admits an extremal Kähler metric whose scalar curvature is strictly less than . Combined with previous observations by Mabuchi and Nakamura in the other direction, this gives a characterization of the existence of Mabuchi solitons in terms of the existence of extremal Kähler metrics on Fano manifolds. An extension of this correspondence to ‐solitons is also obtained.
ISSN:0024-6093
1469-2120
DOI:10.1112/blms.13222