Half conformally flat gradient Ricci almost solitons.

Abstract

The local structure of half conformally flat gradient Ricci almost solitons is investigated, showing that they are locally conformally flat in a neighbourhood 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 κ-Einstein soliton and is realized on the cotangent bundle of an affine surface.