Ricci flat K\"ahler metrics on rank two complex symmetric spaces

TL;DR

This paper constructs Ricci flat K"ahler metrics on rank two complex symmetric spaces using explicit asymptotic models, recovering known metrics and discovering new ones, with implications for geometric analysis.

Contribution

It introduces a method to obtain Ricci flat K"ahler metrics on rank two symmetric spaces, including new metrics beyond previous results.

Findings

Recovered Biquard-Gauduchon metrics in the Hermitian case

Constructed several new Ricci flat K"ahler metrics

Linked asymptotic geometry to the wonderful compactification

Abstract

We obtain Ricci flat K\"ahler metrics on complex symmetric spaces of rank two by using an explicit asymptotic model whose geometry at infinity is interpreted in the wonderful compactification of the symmetric space. We recover the metrics of Biquard-Gauduchon in the Hermitian case and obtain in addition several new metrics.