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arXiv · 1901.09754

Ricci iteration for coupled Kähler-Einstein metrics

Ryosuke Takahashi
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Abstract

In this paper, we introduce the "coupled Ricci iteration", a dynamical system related to the Ricci operator and twisted Kähler-Einstein metrics as an approach to the study of coupled Kähler-Einstein (CKE) metrics. For negative first Chern class, we prove the smooth convergence of the iteration. For positive first Chern class, we also provide a notion of coercivity of the Ding functional, and show its equivalence to existence of CKE metrics. As an application, we prove the smooth convergence of the iteration on CKE Fano manifolds assuming that the automorphism group is discrete.

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BibTeXRIS

Ryosuke Takahashi. 2019-11-18. Ricci iteration for coupled Kähler-Einstein metrics. https://doi.org/10.1093/imrn%2Frnz273

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