Half conformally flat gradient Ricci almost solitons

TL;DR

This paper studies the local structure of half conformally flat gradient Ricci almost solitons, revealing their conformal flatness under certain conditions and characterizing null-gradient cases as steady traceless ff6 Einstein solitons on cotangent bundles.

Contribution

It provides a detailed local classification of half conformally flat gradient Ricci almost solitons, including the null-gradient case as a specific geometric structure.

Findings

They are locally conformally flat where the gradient of the potential is non-null.

Null-gradient solitons are steady traceless ff6 Einstein solitons.

Null-gradient solitons are realized on cotangent bundles of affine surfaces.

Abstract

The local structure of half conformally flat gradient Ricci almost solitons is investigated, showing that they are locally conformally flat in a neighborhood of any point where the gradient of the potential function is non-null. In opposition, if the gradient of the potential function is null, then the soliton is a steady traceless $\kappa$-Einstein soliton and is realized on the cotangent bundle of an affine surface.