https://neckpinch.com/authors/udhav-fowdar/New arXiv papers by Udhav Fowdar, from Neckpinch Tue, 03 Nov 2026 08:41:12 GMT 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 https://neckpinch.com/papers/2502.06066/arxiv:2502.06066Sun, 09 Feb 2025 00:00:00 GMTAnna Fino, Udhav Fowdar — A G₂-structure on a 7-manifold M is called a G₂T-structure if M admits a G₂-connection ∇^T with totally skew-symmetric torsion T_φ. If furthermore, T_φ is closed then it is called a strong G₂T-structure. In this paper we investigate the geometry of (strong) G₂T-manifolds in relation to its curvature, S¹ action and almost Hermitian structures. In particular, we study the Ricci flatness condition of ∇^T and give an equivalent characterisation in terms of geometric properties of the G₂ Lee form. Analogous results are also obtained for almost Hermitian 6-manifolds with skew-symmetric Nijenhuis tensor. Moreover, by considering the S¹ reduction by the dual of the G₂ Lee form, we show that Ricci-flat strong G₂T-structures correspond to solutions of the SU(3) heterotic system on certain almost Hermitian half-flat 6-manifolds. Many explicit examples are described and in particular, we construct the first examples of strong G₂T-structures with ∇^T not Ricci flat. Lastly, we classify G₂-flows inducing gauge fixed solutions to the generalised Ricci flow akin to the pluriclosed flow in complex geometry. The approach is this paper is based on the representation theoretic methods due to Bryant.Ricci flowGeneralized & G₂ flowsRicci-flat & Calabi–Yau