New examples of shrinking Laplacian solitons

2020/06/23 by Nicolini, Marina
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2006.13074

Abstract

We give a one-parameter family of examples of shrinking Laplacian solitons, which are the second known solutions to the closed G₂-Laplacian flow with a finite-time singularity. The torsion forms and the Laplacian and Ricci operators of a large family of G₂-structures on different Lie groups are also studied. We apply these formulas to prove that, under a suitable extra condition, there is no closed eigenform for the Laplacian on such family.

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