https://neckpinch.com/authors/ramiro-lafuente/New arXiv papers by Ramiro Lafuente, from Neckpinch Tue, 03 Nov 2026 07:15:30 GMT https://arxiv.org/abs/2608.25619arxiv:2608.25619Wed, 26 Aug 2026 00:00:00 GMTElia Fusi, Ramiro A. Lafuente, James Stanfield — We relate the generalized Ricci curvature of left-invariant generalized metrics on a Lie group with the Ricci curvature of certain metric Lie algebras. As an application, we prove subconvergence of rescaled generalized Ricci flows to expanding generalized Ricci solitons on simply connected Lie groups with positive semi-definite Killing form. Under the same hypotheses, subconvergence of pluriclosed flows to expanding pluriclosed solitons is also shown. We further prove that left-invariant Bismut-Ricci flat metrics arise as critical points for the generalized scalar curvature functional on unimodular Lie groups. In view of this, we establish dynamical stability for the generalized Ricci flow of so-called standard bi-invariant, Bismut-flat metrics on compact, simply connected, semisimple Lie groups and construct examples of dynamically unstable Bismut-flat metrics which are non-standard.Ricci flowGeneralized & G₂ flowsRicci solitonsRicci-flat & Calabi–YauScalar curvatureHomogeneous spacesStability & uniqueness https://arxiv.org/abs/2506.11362arxiv:2506.11362Thu, 12 Jun 2025 00:00:00 GMTRamiro A. Lafuente, Adam Thompson — Motivated by the long-time behavior of Ricci flows that collapse with bounded curvature, we study expanding Ricci solitons with nilpotent symmetry on vector bundles over a closed manifold. We prove that, under mild assumptions that are satisfied by Ricci flow limits, the equations dimension-reduce to the so-called twisted harmonic-Einstein equations. When the base is a surface, we establish a correspondence between solutions of the latter and a class of G-Higgs bundles. This allows us to produce infinite families of new examples that are not locally homogeneous, and in particular to obtain a complete description in dimension 4. We also show that all our examples admit Einstein one-dimensional extensions.Ricci flowRicci solitons4-manifoldsHomogeneous spacesLong-time existence & convergence https://arxiv.org/abs/2404.15749arxiv:2404.15749Wed, 24 Apr 2024 00:00:00 GMTElia Fusi, Ramiro A. Lafuente, James Stanfield — We develop a framework inspired by Lauret's "bracket flow" to study the generalized Ricci flow, as introduced by Streets, on discrete quotients of Lie groups. As a first application, we establish global existence on solvmanifolds in arbitrary dimensions, a result which is new even for the pluriclosed flow. We also define a notion of generalized Ricci soliton on exact Courant algebroids that is geometrically meaningful and allows for non-trivial expanding examples. On nilmanifolds, we show that these solitons arise as rescaled limits of the generalized Ricci flow, provided the initial metrics have "harmonic torsion", and we classify them in low dimensions. Finally, we provide a new formula for the generalized Ricci curvature of invariant generalized metrics in terms of a moment map for the action of a non-reductive real Lie group.Ricci flowGeneralized & G₂ flowsRicci solitonsHomogeneous spacesLong-time existence & convergence https://arxiv.org/abs/2302.04964arxiv:2302.04964Thu, 09 Feb 2023 00:00:00 GMTTheodora Bourni, Timothy Buttsworth, Ramiro Lafuente, Mat Langford — For each n≥ 3, we construct a 'pancake-like', O(2)× O(n-1)-invariant ancient Ricci flow with positive curvature operator and bounded "girth", and we determine its asymptotic limits backwards in time. This solution is new even in dimension three. The construction hinges on the Ricci flow invariance of certain conditions on the curvature and its spatial derivatives under this symmetry regime, whose proof does not follow from Hamilton's tensor maximum principle.Ricci flowAncient solutions3-manifoldsSphere theorems