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arXiv · 2601.10730

Ricci Solitons of Left-Invariant Metrics on Lie Groups with Derived Algebra of Dimension at Most Two

Hamid Reza Salimi Moghaddam
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Abstract

In this article, we investigate when a left-invariant Riemannian metric on a Lie group is a Ricci soliton, under the assumption that the derived algebra has dimension at most two. We establish computable necessary and sufficient conditions for a given left-invariant Riemannian metric to be a Ricci soliton. As applications, we obtain several examples of Ricci nilsolitons and apply our results to indecomposable Lie groups of dimension at least five with two-dimensional derived algebra.

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Hamid Reza Salimi Moghaddam. 2026-09-12. Ricci Solitons of Left-Invariant Metrics on Lie Groups with Derived Algebra of Dimension at Most Two. https://arxiv.org/abs/2601.10730

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