https://neckpinch.com/authors/beatrice-brienza/New arXiv papers by Beatrice Brienza, from Neckpinch Tue, 03 Nov 2026 08:41:12 GMT https://neckpinch.com/papers/2608.14358/arxiv:2608.14358Fri, 14 Aug 2026 00:00:00 GMTBeatrice Brienza, Jeffrey Streets — We identify a Hermitian curvature flow which preserves HKT geometry, and whose fixed points are HKT-Einstein metrics, equivalent to a flow suggested by Verbitsky in the context of the quaternionic Monge-Ampère equation. We exhibit a fundamental regularity obstruction and a monotonicity formula for the Chern scalar curvature. We formulate a maximal existence time conjecture for this flow, and give a conditional resolution. We establish the existence conjecture in dimension four. We show the existence of a divergent sequence of HKT-Einstein metrics on quaternionic Hopf surfaces. These are the first non-homogeneous examples in the literature, and indicate the delicacy of the convergence question. Finally we classify which strong HKT structures arising from bi-invariant metrics on Lie groups are also HKT-Einstein.Generalized & G₂ flowsEinstein metrics4-manifoldsKähler geometryScalar curvatureHomogeneous spaces https://neckpinch.com/papers/2608.08781/arxiv:2608.08781Sun, 09 Aug 2026 00:00:00 GMTBeatrice Brienza, Anna Fino, Udhav Fowdar, Gueo Grantcharov — Motivated by the analogy with the Bismut connection in Hermitian geometry, we study Sasaki with torsion manifolds. In particular, we characterize co-Kähler-like and flat Sasaki with torsion manifolds, and we introduce the notion of a ∇-Einstein manifold as the odd-dimensional analogue of the Bismut Hermite-Einstein condition. We provide non-compact examples and we study compact ∇-Einstein manifold in dimension 5 and 7. We also develop a general framework for geometric flows of almost contact metric structures. In particular, we derive a flow for Sasaki with torsion structures that preserves the strong condition, that is, the closure of the torsion. Furthermore we prove that such flow is gauge-equivalent to the generalized Ricci flow and it is gauge-equivalent to the pluriclosed flow, after performing a trivial product with S¹.Ricci flowGeneralized & G₂ flowsEinstein metricsKähler geometryBoundaries & non-compactSasakian & contact geometry