Coupled Kähler-Ricci solitons on toric Fano manifolds

Abstract

We prove a necessary and sufficient condition in terms of the barycenters of a collection of polytopes for existence of coupled Kähler-Einstein metrics on toric Fano manifolds. This confirms the toric case of a coupled version of the Yau-Tian-Donaldson conjecture. We also obtain a necessary and sufficient condition for existence of torus-invariant solutions to a system of soliton type equations on toric Fano manifolds. Some of these solutions provide natural candidates for the large time limits of a certain geometric flow generalizing the Kähler-Ricci flow.

29 pages. Changed title. Added example of coupled Kähler-Einstein metric on manifold that don't admit Kähler-Einstein metrics

References in corpus (1)

• Kähler-Einstein metrics on group compactifications

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