Einstein Hermitian Metrics of Non Negative Sectional Curvature

TL;DR

This paper classifies certain four-dimensional Hermitian Einstein manifolds with non-negative sectional curvature, showing they are isometric to either complex projective space with Fubini-Study metric or the product of two spheres.

Contribution

It provides a complete classification of simply connected Hermitian Einstein 4-manifolds with non-negative sectional curvature, identifying them explicitly.

Findings

Such manifolds are isometric to $\mathbb{C} ext{P}^2$ with Fubini-Study metric

Or they are isometric to $ ext{S}^2 imes ext{S}^2$ with the canonical metric

The classification confirms the geometric structure of these special manifolds.

Abstract

We prove that a simpy connected Hermitian Einstein 4-manifold with non-negative sectional curvature is isometric to complex projective space $\mathbb{C}\mathbb{P}^{2}$ with the Fubini-Study metric or isometric to the product $\mathbb{S}^{2}\times \mathbb{S}^{2}$ with the canonical metric.