https://neckpinch.com/authors/ernani-ribeiro/New arXiv papers by Ernani Ribeiro, from Neckpinch Tue, 03 Nov 2026 07:15:30 GMT https://arxiv.org/abs/2610.40994arxiv:2610.40994Thu, 29 Oct 2026 00:00:00 GMTErnani Ribeiro, Hung Tran — We classify complete, non-compact, simply connected, irreducible four-dimensional steady gradient Ricci solitons that are globally conformally Kähler and have an isoparametric potential. The steady Ricci solitons are U(2)-invariant nuts on ℝ⁴, including the Bryant and Cao solitons, and bolts on S² × ℝ² and on 𝓞(−m)→ℂP}¹. For each m≥3 there is exactly one non-collapsed bolt. A key step, valid for Ricci solitons of every sign, is that away from the locally conformally flat case, the conformal factor is aligned with the potential function, which yields cohomogeneity-one symmetry.Ricci solitonsKähler–Ricci solitons(Non)collapsing4-manifoldsKähler geometryHomogeneous spacesBoundaries & non-compact https://arxiv.org/abs/2509.20669arxiv:2509.20669Thu, 25 Sep 2025 00:00:00 GMTXiaodong Cao, Ernani Ribeiro, Hosea Wondo — We investigate four-dimensional gradient shrinking Ricci solitons with positive modified sectional curvature. Our first main result shows that if the norm of the self-dual Weyl tensor and the scalar curvature satisfy a certain sharp pinching condition (closely related, in a precise sense, to that of Kähler metric), then the soliton is necessarily locally Kähler. We further obtain a characterization theorem and a weighted integral gap result for compact gradient shrinking Ricci solitons with bounded modified sectional curvature. In addition, we establish a Hitchin-Thorpe type inequality for compact four-dimensional Ricci solitons, providing new topological constraints on such manifolds.Ricci solitonsCurvature pinching4-manifoldsKähler geometryScalar curvature https://arxiv.org/abs/2212.05267arxiv:2212.05267Sat, 10 Dec 2022 00:00:00 GMTXiaodong Cao, Ernani Ribeiro, Hung Tran — In this article, we investigate four-dimensional gradient shrinking Ricci solitons close to a Kähler model. The first theorem could be considered as a rigidity result for the Kähler-Ricci soliton structure on S²× ℝ² (in the sense of Remark 1). Moreover, we show that if the quotient of norm of the self-dual Weyl tensor and scalar curvature is close to that on a Kähler metric in a specific sense, then the gradient Ricci soliton must be either half-conformally flat or locally Kähler.Ricci solitonsKähler–Ricci solitons4-manifoldsKähler geometryScalar curvatureStability & uniqueness https://arxiv.org/abs/2203.14916arxiv:2203.14916Mon, 28 Mar 2022 00:00:00 GMTXu Cheng, Ernani Ribeiro, Detang Zhou — In this article, we investigate the geometry of 4-dimensional compact gradient Ricci solitons. We prove that, under an upper bound condition on the range of the potential function, a 4-dimensional compact gradient Ricci soliton must satisfy the classical Hitchin-Thorpe inequality. In addition, some volume estimates are also obtained.Ricci solitons4-manifolds