Codimension one Ricci soliton subgroups of solvable Iwasawa groups

TL;DR

This paper classifies codimension one Ricci soliton subgroups within solvable Iwasawa groups, extending understanding of Ricci solitons in various geometric contexts and building on recent embedding results.

Contribution

It provides a comprehensive classification of codimension one Ricci soliton subgroups in solvable Iwasawa groups, Damek-Ricci spaces, and generalized Heisenberg groups.

Findings

Classified Ricci soliton subgroups in Iwasawa groups of symmetric spaces.

Extended classification to Damek-Ricci spaces.

Extended classification to generalized Heisenberg groups.

Abstract

Recently, Jablonski proved that, to a large extent, a simply connected solvable Lie group endowed with a left-invariant Ricci soliton metric can be isometrically embedded into the solvable Iwasawa group of a non-compact symmetric space. Motivated by this result, we classify codimension one subgroups of the solvable Iwasawa groups of irreducible symmetric spaces of non-compact type whose induced metrics are Ricci solitons. We also obtain the classifications of codimension one Ricci soliton subgroups of Damek-Ricci spaces and generalized Heisenberg groups.