A note on four dimensional (anti-)self-dual quasi-Einstein manifolds

TL;DR

This paper proves that complete four-dimensional anti-self-dual or self-dual quasi-Einstein manifolds are either Einstein or locally conformally flat, extending recent results in the field.

Contribution

It generalizes previous work by showing a broader classification of four-dimensional quasi-Einstein manifolds with (anti-)self-duality.

Findings

Complete four-dimensional (anti-)self-dual quasi-Einstein manifolds are Einstein or locally conformally flat.

Extends recent classification results in geometric analysis.

Provides new insights into the structure of special Einstein manifolds.

Abstract

In this short note we prove that any complete four dimensional anti-self-dual (or self-dual) quasi-Einstein manifolds is either Einstein or locally conformally flat. This generalizes a recent result of X. Chen and Y. Wang.