Homogeneous Ricci almost solitons

TL;DR

This paper classifies locally homogeneous proper Ricci almost solitons, showing they are either of constant sectional curvature or a product space involving a space of constant curvature.

Contribution

It provides a complete classification of locally homogeneous proper Ricci almost solitons, identifying their geometric structure.

Findings

Proper Ricci almost solitons are either of constant sectional curvature or products with a space of constant curvature.

The classification simplifies understanding of the geometric structure of such solitons.

The results extend the theory of Ricci solitons to a broader class of almost solitons.

Abstract

It is shown that a locally homogeneous proper Ricci almost soliton is either of constant sectional curvature or a product $\mathbb{R}\times N(c)$, where $N(c)$ is a space of constant curvature.