Three-dimensional homogeneous generalized Ricci solitons

TL;DR

This paper classifies three-dimensional homogeneous generalized Ricci solitons on Lie groups, covering both Riemannian and Lorentzian cases, providing a comprehensive understanding of their structure.

Contribution

It offers a complete classification of left-invariant generalized Ricci solitons on three-dimensional Lie groups in both Riemannian and Lorentzian geometries.

Findings

Classification of homogeneous models achieved

Explicit descriptions of solitons on Lie groups provided

Unified treatment for Riemannian and Lorentzian cases

Abstract

We study three-dimensional generalized Ricci solitons, both in Riemannian and Lorentzian settings. We shall determine their homogeneous models, classifying left-invariant generalized Ricci solitons on three-dimensional Lie groups.