https://neckpinch.com/authors/qiaoling-xia/New arXiv papers by Qiaoling Xia, from Neckpinch Tue, 03 Nov 2026 08:37:45 GMT https://neckpinch.com/papers/2403.02038/arxiv:2403.02038Mon, 04 Mar 2024 00:00:00 GMTQiaoling Xia — In this paper, (gradient) almost Ricci solitons on Finsler measure spaces (M, F, m) are introduced and investigated. We prove that (M, F, m) is a gradient almost Ricci soliton if and only if the infinity-Ricci curvature Ric_∞ is a scalar function on M when M is compact. Moreover, we give an equivalent characterization of (gradient) almost Ricci solitons for Randers metrics F=α+β, which implies that every Randers (gradient) almost Ricci soliton is of isotropic S_BH-curvature. Based on this and the navigation technique, we further classify Randers almost Ricci solitons (resp. gradient almost Ricci solitons) up to classifications of Randers Einstein metrics F (resp. Riemannian gradient almost Ricci solitons) and the homothetic vector fields of F (resp. solutions of the equation which the weight function f of m satisfies) when F has isotropic S_BH-curvature. As applications, we obtain some rigidity results for compact Randers (gradient) Ricci solitons and construct several Randers gradient Ricci solitons, which are the first nontrivial examples of gradient Ricci solitons in Finsler geometry.Ricci solitonsEinstein metricsAlmost & η-Ricci solitonsStability & uniqueness