On homogeneous closed gradient Laplacian solitons

2023/02/22 by Ng, Nicholas
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2302.11441

Abstract

We prove a structure theorem for homogeneous closed gradient Laplacian solitons and use it to show some examples of closed Laplacian solitons cannot be made gradient. More specifically, we show that the Laplacian solitons on nilpotent Lie groups found by Nicolini are not gradient up to homothetic G₂-structures except for N₁, where f must be a Gaussian. We also show that the closed G₂-structure φ₁₂ on N₁₂ constructed by Fernández-Fino-Manero cannot be a gradient soliton. We further show that closed non-torsion-free gradient Laplacian solitons on almost abelian solvmanifolds are isometric to products N × \mathbb R^k with f constant on N.

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