Remarks on the existence of bilaterally symmetric extremal K\"ahler metrics on $\mathbb{CP}^2\sharp 2\bar{\mathbb{CP}^2}$

TL;DR

This paper investigates the existence of bilaterally symmetric extremal Kähler metrics on the complex surface obtained by blowing up the complex projective plane at two points, contributing to the understanding of special metrics in complex geometry.

Contribution

It demonstrates the existence of such extremal Kähler metrics on the specified complex surface, providing new insights into their geometric properties.

Findings

Existence of bilaterally symmetric extremal Kähler metrics established

Advances understanding of extremal metrics on complex blow-ups

Contributes to classification of special Kähler metrics

Abstract

In this short note we show that the existence of bilaterally symmetric extremal K\"ahler metrics on $\mathbb{CP}^2\sharp 2\bar{\mathbb{CP}^2}$.