Toric extremal Kähler-Ricci solitons are Kähler-Einstein

Abstract

In this short note, we prove that a Calabi extremal Kähler-Ricci soliton on a compact toric Kähler manifold is Einstein. This settles for the class of toric manifolds a general problem stated by the authors that they solved only under some curvature assumptions.

Keywords

• extremal kähler metrics
• kähler-ricci solitons
• einstein manifolds
• toric manifolds
• 53c25
• 53c55
• 58d19