Randers Ricci soliton homogeneous nilmanifolds

Abstract

Let $F$ be a left-invariant Randers metric on a simply connected nilpotent Lie group $N$, induced by a left-invariant Riemannian metric $\hat{\boldsymbol{a}}$ and a vector field $X$ which is $I_{\hat{\boldsymbol{a}}}(M)$-invariant. We show that 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.