Hamid Reza Salimi Moghaddam — Neckpinchhttps://neckpinch.com/authors/hamid-reza-salimi-moghaddam/New arXiv papers by Hamid Reza Salimi Moghaddam, from Neckpinch Tue, 03 Nov 2026 08:41:12 GMT Ricci Solitons of Left-Invariant Metrics on Lie Groups with Derived Algebra of Dimension at Most Twohttps://neckpinch.com/papers/2601.10730/arxiv:2601.10730Mon, 05 Jan 2026 00:00:00 GMTHamid Reza Salimi Moghaddam — 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.Ricci solitonsSurfacesHomogeneous spaces