Abstract
We prove that a radial Kähler metric $g$ is Kähler-Einstein if and only if one of the following conditions is satisfied: 1. $g$ is extremal and it is associated to a Kähler-Ricci soliton; 2. two different generalized scalar curvatures of $g$ are constant; 3. $g$ is extremal (not cscK) and one of its generalized scalar curvature is constant.
Funding Statement
The first and the third authors were supported by STAGE - Funded by Fondazione di Sardegna and by KASBA- Funded by Regione Autonoma della Sardegna. The second author was supported by PRIN 2017 “Real and Complex Manifolds: topology, geometry and holomorphic dynamics" and MIUR grant “Dipartimenti di Eccellenza 2018-2022". All the three authors were supported by INdAM GNSAGA - Gruppo Nazionale per le Strutture Algebriche, Geometriche e le loro Applicazioni.
Citation
Andrea Loi. Filippo Salis. Fabio Zuddas. "On canonical radial Kähler metrics." Osaka J. Math. 60 (3) 545 - 554, July 2023.
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