https://neckpinch.com/authors/youssef-ayad/New arXiv papers by Youssef Ayad, from Neckpinch Tue, 03 Nov 2026 07:15:30 GMT https://arxiv.org/abs/2609.17183arxiv:2609.17183Tue, 15 Sep 2026 00:00:00 GMTYoussef Ayad — There exist three nonequivalent left invariant Lorentzian metrics on the Heisenberg group H₂ₙ₊₁, or equivalently, three nonequivalent Lorentzian inner products on the Heisenberg Lie algebra h₂ₙ₊₁, denoted by μ, ν, and φ. We show that, in a specific case, μ is an algebraic Ricci soliton that is shrinking. Moreover, ν is an algebraic Ricci soliton only on the three-dimensional Heisenberg Lie algebra h₃ and it is shrinking. Finally, we show that φ is a steady algebraic Ricci soliton on h_(2n + 1) for n > 1. However, for n = 1, φ is flat.Ricci solitons3-manifoldsPhysics https://arxiv.org/abs/2608.08370arxiv:2608.08370Sat, 08 Aug 2026 00:00:00 GMTYoussef Ayad — In this paper, we compute the canonical and Kobayashi-Nomizu connections, together with their curvature, on Lorentzian four-dimensional nilpotent Lie groups endowed with a product structure. We also classify the algebraic Ricci solitons associated with these connections.Ricci solitons4-manifoldsHomogeneous spacesPhysics https://arxiv.org/abs/2601.15008arxiv:2601.15008Wed, 21 Jan 2026 00:00:00 GMTYoussef Ayad — 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.Ricci solitons4-manifoldsHomogeneous spaces