https://neckpinch.com/authors/abdou-bousso/New arXiv papers by Abdou Bousso, from Neckpinch Tue, 03 Nov 2026 07:15:30 GMT https://arxiv.org/abs/2609.14866arxiv:2609.14866Mon, 14 Sep 2026 00:00:00 GMTAbdou Bousso, Ameth Ndiaye — We study the iterated action of the Lie derivative on the curvature tensor of a Riemannian manifold with rank-one anisotropic curvature, whose Riemann tensor is expressed via the Kulkarni-Nomizu product as R = λ(ξ^flat⊗ξ^flat)owedge g. First, we examine the conditions under which such a manifold admits a Ricci soliton structure and demonstrate that this property implies the almost θ-Yamabe soliton structure. Furthermore, we show that if the associated potential vector field X is a symmetry of the Ricci tensor of a fixed order k (i.e., 𝓛_X^k Ric = 0), the geometric problem reduces to solving a partial differential equation of order k+1 along the flow. Finally, under the assumption that X is a conformal vector field (𝓛_X g = 2φg) whose infinitesimal flow preserves the line distribution 𝓓=Span\ξ\ (with [X,ξ]=aξ for a∈ℝ), we prove that several key geometric problems (such as establishing the relation 𝓛_X^k R = R, determining the minimal order k for X to be a Lie curvature symmetry, or satisfying 𝓛_X^(k+1)R = f 𝓛_X^k R for a continuous function f) are equivalent to a scalar differential problem governed by the operator D_X = X + 6φ+ 2a.Anisotropic & nonlocal flowsRicci solitonsAlmost & η-Ricci solitons https://arxiv.org/abs/2609.12237arxiv:2609.12237Thu, 10 Sep 2026 00:00:00 GMTAbdou Bousso, Ameth Ndiaye — In this article, we study Ricci-Yamabe solitons on the Lie group Sol × ℝⁿ equipped with a natural left-invariant Riemannian metric, explicitly determining the vector fields that characterize them. We then deduce that, in the case of a Ricci soliton, it is expanding, whereas in the case of a Yamabe soliton, it is shrinking. Finally, we show that if this Lie group is a gradient Ricci-Yamabe soliton, the vector field belongs to Span\∂_(t₁), …, ∂_(tₙ)\, and we explicitly provide the Perelman potential.Ricci solitonsAlmost & η-Ricci solitonsHomogeneous spaces https://arxiv.org/abs/2510.12745arxiv:2510.12745Tue, 14 Oct 2025 00:00:00 GMTMafal Ndiaye Diop, Abdou Bousso, Cheikh Khoule, Ameth Ndiaye — The objective of this paper is to deepen the study of vector fields on hyperbolic spaces ℍⁿ that transform them into a Ricci-Bourguignon soliton. Starting from a recent work in which characterizes these fields as Killing fields of a specific shape, we propose a detailed geometric study of their structure and behavior in the dimensions n=2, 3 and n≥ 3. In odd dimension we show that the dual form of these vectors are contact forms. This work aims to enrich the understanding of self-similar solutions of the Ricci flow in a more general context.Ricci flowAlmost & η-Ricci solitons https://arxiv.org/abs/2505.02145arxiv:2505.02145Sun, 04 May 2025 00:00:00 GMTAbdou Bousso, Ameth Ndiaye — In this paper, we characterize the Ricci soliton equations on the Poincaré upper half plane . First we classify all Ricci soliton and Ricci Bourguignon soliton in the half plane of Poincaré and after we generalize those equations in ℍⁿ. We obtain some nice properties of the soliton about their geodesic flows.Ricci solitonsAlmost & η-Ricci solitons