Toric extremal Kaehler-Ricci solitons are Kaehler-Einstein

TL;DR

This paper proves that on compact toric Kähler manifolds, Calabi extremal Kähler-Ricci solitons must be Einstein, resolving a broader problem in the classification of such geometric structures.

Contribution

It establishes that all Calabi extremal Kähler-Ricci solitons on compact toric Kähler manifolds are necessarily Einstein, removing previous curvature assumptions.

Findings

Calabi extremal Kähler-Ricci solitons are Einstein on toric manifolds

The result applies to all compact toric Kähler manifolds

Solves a general problem in the classification of Kähler-Ricci solitons

Abstract

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