# Invariant Solutions for Gradient Ricci Almost Solitons

## TL;DR

This paper classifies certain invariant conformal metrics as gradient Ricci almost solitons, expanding understanding of their geometric properties in pseudo-Euclidean and Euclidean spaces.

## Contribution

It demonstrates that all conformal metrics invariant under translation or rotation in specific spaces are gradient Ricci almost solitons, providing new classifications in differential geometry.

## Key findings

- Invariant conformal metrics under translation are gradient Ricci almost solitons.
- Conformal metrics invariant under rotation in Euclidean space are gradient Ricci almost solitons.
- The results include metrics on pseudo-Euclidean and product manifolds with Ricci-flat components.

## Abstract

In this paper we show that all conformal metrics to a pseudo-euclidean space invariant under the translation group, and all the conformal metrics product manifold also invariant by translation where F m it is Ricci flat semi-Riemannian manifold, are gradient Ricci almost soliton. We also proved that all conformal metrics to a euclidean space and invariant by rotation are gradient Ricci almost soliton.