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In 2002, using a variational method, Lauret classified five-dimensionalnilsolitons. In this work, using the algebraic Ricci soliton equation, weobtain the same classification. We show that, among ten classes offive-dimensional nilmanifolds, seven classes admit Ricci soliton structure. Inany case, the derivation which satisfies the algebraic Ricci soliton equationis computed.

On the classification of five-dimensional nilsolitons