On the classification of five-dimensional nilsolitons

TL;DR

This paper re-derives Lauret's 2002 classification of five-dimensional nilsolitons using algebraic Ricci soliton equations, identifying seven classes with Ricci soliton structures.

Contribution

It provides an alternative algebraic Ricci soliton approach to classify five-dimensional nilsolitons, confirming prior results with a different method.

Findings

Seven of ten nilmanifold classes admit Ricci soliton structures

The algebraic Ricci soliton equations are explicitly solved for these classes

The classification matches Lauret's 2002 results

Abstract

In 2002, using a variational method, Lauret classified five-dimensional nilsolitons. In this work, using the algebraic Ricci soliton equation, we obtain the same classification. We show that, among ten classes of five-dimensional nilmanifolds, seven classes admit Ricci soliton structure. In any case, the derivation which satisfies the algebraic Ricci soliton equation is computed.