Abstract
We investigate the existence of closed $G_2$-structures which are solitons for the Laplacian flow on nilpotent Lie groups. We obtain that seven of the twelve Lie algebras admitting a closed $G_2$-structure do admit a Laplacian soliton. Moreover, one of them admits a continuous family of Laplacian solitons which are pairwise non-homothetic and the Laplacian flow evolution on four of the Lie groups is not diagonal.
Citation
Marina Nicolini. "Laplacian solitons on nilpotent Lie groups." Bull. Belg. Math. Soc. Simon Stevin 25 (2) 183 - 196, june 2018. https://doi.org/10.36045/bbms/1530065008
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