A splitting theorem on toric varieties

TL;DR

This paper proves that extremal Kaehler metrics on product toric varieties decompose into product metrics, using the short time existence of the Calabi flow, advancing understanding of geometric structures on toric varieties.

Contribution

It establishes a splitting theorem for extremal Kaehler metrics on product toric varieties, linking geometric flow methods to metric decomposition.

Findings

Extremal Kaehler metrics on product toric varieties are products of extremal metrics.

The Calabi flow's short time existence is used to prove the splitting theorem.

The result enhances understanding of the structure of extremal metrics on complex manifolds.

Abstract

Using the short time existence of the Calabi flow, we prove that any extremal Kaehler metric on a product toric variety is a product extremal Kaehler metric.