# Noncompact quasi-Einstein manifolds conformal to a Euclidean space

## TL;DR

This paper classifies nontrivial $m$-quasi-Einstein manifolds conformal to Euclidean space, focusing on cases with specific invariance properties and parameters, providing a comprehensive understanding of their structure.

## Contribution

It offers a complete classification of such manifolds under invariance assumptions for particular parameter values, advancing the understanding of quasi-Einstein geometry.

## Key findings

- Classification when $oxed{ ext{lambda}=0}$ and $m
eq 0$
- Explicit description of conformal factors and potential functions
- Results applicable to manifolds with symmetry under translation groups

## Abstract

The goal of this article is to investigate nontrivial $m$-quasi-Einstein manifolds globally conformal to an $n$-dimensional Euclidean space. By considering such manifolds, whose conformal factors and potential functions are invariant under the action of an $(n-1)$-dimensional translation group, we provide a complete classification when $\lambda=0$ and $m\geq 1$ or $m=2-n.$