Codimension one Ricci soliton subgroups of nilpotent Iwasawa groups

TL;DR

This paper classifies codimension one Ricci soliton subgroups within nilpotent Iwasawa groups, which are key in understanding the structure of certain homogeneous Ricci solitons and Einstein manifolds.

Contribution

It provides a complete classification of codimension one Ricci soliton subgroups in nilpotent Iwasawa groups, advancing the understanding of their geometric and algebraic properties.

Findings

Classification of codimension one Ricci soliton subgroups achieved

Identification of geometric structures supporting Ricci solitons

Insights into the relation between Lie subgroups and Ricci soliton metrics

Abstract

Any expanding homogeneous Ricci soliton (in particular any homogeneous Einstein manifold of negative scalar curvature) can be obtained, up to isometry, from a Lie subgroup of a nilpotent Iwasawa group $N$ whose induced metric is a Ricci soliton. By nilpotent Iwasawa group we mean the nilpotent Lie group $N$ of the Iwasawa decomposition associated with a symmetric space of non-compact type. Motivated by this fact, in this paper we classify codimension one Lie subgroups of any nilpotent Iwasawa group $N$ whose induced metric is a Ricci soliton.