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arXiv · 2607.26240

Ricci Solitons on the Lie Group $Sol^3_{m,n}$ and Applications

Mohammed El Amine Mekki·Ahmed Mohammed Cherif
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Abstract

In this paper, we study Ricci solitons on the three-dimensional solvable Lie group $\mathrm{Sol}^{3}_{m,n}$ equipped with a left-invariant Riemannian metric, viewed as a generalization of the classical $\mathrm{Sol}^{3}$ geometry. We investigate harmonic maps, harmonic sections, and geodesic curves, including the geodesic properties of the integral curves of the Ricci soliton vector field. We also characterize harmonic linear maps from $\mathrm{Sol}^{3}_{m,n}$ into Euclidean spaces.

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Mohammed El Amine Mekki, Ahmed Mohammed Cherif. 2026-07-28. Ricci Solitons on the Lie Group $Sol^3_{m,n}$ and Applications. https://arxiv.org/abs/2607.26240

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