# Randers Ricci soliton homogeneous nilmanifolds

## TL;DR

This paper characterizes Randers Ricci solitons on homogeneous nilmanifolds, showing they are equivalent to semialgebraic Ricci solitons under certain conditions, thus advancing understanding of geometric flows on these spaces.

## Contribution

It establishes a precise equivalence between Ricci solitons and semialgebraic Ricci solitons for Randers metrics on nilpotent Lie groups, under flow conditions.

## Key findings

- Ricci flow solutions are unique for the considered metrics
- Randers Ricci solitons correspond to semialgebraic Ricci solitons
- Characterization of Ricci solitons on nilpotent Lie groups

## Abstract

Let $F$ be a left invariant Randers metric on a simply connected nilpotent Lie group $N$, induced by a left invariant Riemannian metric ${\hat{\textbf{\textit{a}}}}$ and a vector field $X$ which is $I_{\hat{\textbf{\textit{a}}}}(M)$-invariant. If the Ricci flow equation has a unique solution then, $(N,F)$ is a Ricci soliton if and only if $(N,F)$ is a semialgebraic Ricci soliton.