Four-dimensional pseudo-Riemannian homogeneous Ricci solitons

TL;DR

This paper classifies four-dimensional homogeneous pseudo-Riemannian Ricci solitons, revealing new non-compact examples that are not solvmanifolds and identifying conformally flat cases that are not symmetric.

Contribution

It provides a complete classification of four-dimensional homogeneous pseudo-Riemannian Ricci solitons with non-trivial isotropy, including novel examples beyond solvmanifolds.

Findings

Existence of non-compact homogeneous Ricci solitons not isometric to solvmanifolds

Identification of conformally flat homogeneous Ricci solitons that are not symmetric

Complete classification of four-dimensional homogeneous pseudo-Riemannian Ricci solitons

Abstract

We consider four-dimensional homogeneous pseudo-Riemannian manifolds with non-trivial isotropy and completely classify the cases giving rise to non-trivial homogeneous Ricci solitons. In particular, we show the existence of non-compact homogeneous (and also invariant) pseudo-Riemannian Ricci solitons which are not isometric to solvmanifolds, and of conformally flat homogeneous pseudo-Riemannian Ricci solitons which are not symmetric.