We prove that a radial Kahler metric g is Kahler-Einstein if and only if one of the following conditions is satisfied: 1. g is extremal and it is associated to a Kahler-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.
On canonical radial Kahler metrics
A. Loi;F. Salis;F. Zuddas
2023-01-01
Abstract
We prove that a radial Kahler metric g is Kahler-Einstein if and only if one of the following conditions is satisfied: 1. g is extremal and it is associated to a Kahler-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.
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