AN ALGEBRAIC PROOF OF THE CLASSIFICATION OF FIVE-DIMENSIONAL NILSOLITONS

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 connected and simply connected nilmanifolds, seven classes admit the Ricci soliton structure. Furthermore, we compute the derivation that satisfies the algebraic Ricci soliton equation in each case.. © 2024 Iranian Mathematical Society.