Survey explores existence conditions for coupled Kähler-Einstein metrics and weighted solitons on Fano manifolds, indicating their algebraic connections.
We consider coupled Kähler-Einstein metrics and weighted solitons on Fano manifolds. These are natural generalizations of Kähler-Einstein metrics. As in the case of Kähler-Einstein metrics, the existence is known to be equivalent to algebraic conditions which generalize the K-polystability. In this survey, we outline recent developments for these two cases.
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Akito Futaki (2026) studied this question.
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