Pseudo-Riemannian Algebraic Ricci Solitons on Four-Dimensional Lie Groups

Youssef Ayad

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arXiv · 2601.15008

Pseudo-Riemannian Algebraic Ricci Solitons on Four-Dimensional Lie Groups

Youssef Ayad

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Abstract

We investigate the conditions under which pseudo-Riemannian inner products induce pseudo-Riemannian algebraic Ricci solitons on four-dimensional Lie algebras. By analyzing the algebraic Ricci soliton equation for each four-dimensional Lie algebra, we obtain a complete description of when such pseudo-Riemannian algebraic Ricci solitons arise in dimension four. We present two applications of our formalism on a chosen four-dimensional Lie algebra by exhibiting a pseudo-Riemannian algebraic Ricci soliton and a flat pseudo-Riemannian inner product, which is a trivial algebraic Ricci soliton.

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Youssef Ayad. 2026-01-21. Pseudo-Riemannian Algebraic Ricci Solitons on Four-Dimensional Lie Groups. https://arxiv.org/abs/2601.15008

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