Laplacian solitons on nilpotent Lie groups

2016/08/30 by Nicolini, Marina
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1608.08599

Abstract

We investigate the existence of closed G₂-structures which are solitons for the Laplacian flow on nilpotent Lie groups. We obtain that seven of the twelve Lie algebras admitting a closed G₂-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 of four of them is not diagonal.

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