5 papers · 1 filter
Local Topological Constraints on Berry Curvature in Spin--Orbit Coupled BECs
Alexander Pigazzini, Magdalena Toda
We establish a local topological obstruction to flattening Berry curvature in spin-orbit-coupled Bose-Einstein condensates (SOC BECs), valid even when the global Chern number vanis…
Cohomologically Calibrated Affine Connections and Forced Irreducibility
Alexander Pigazzini, Magdalena Toda
We establish a principle of forced geometric irreducibility on product manifolds. We prove that for any product manifold , a cohomologically calibrated affine conn…
Cohomological Calibration and Curvature Constraints on Product Manifolds: A Topological Lower Bound
Alexander Pigazzini, Magdalena Toda
We establish a quantitative relationship between mixed de Rham classes and the geometric complexity of metric connections with totally skew torsion on product manifolds where both…
Cohomologically calibrated affine connections and the Einstein condition on
Alexander Pigazzini, Magdalena Toda
This paper applies the recently developed framework of cohomologically calibrated affine connections to the fundamental problem of constructing non-Riemannian Einstein manifolds. I…
Positive biorthogonal curvature on via affine connection
Alexander Pigazzini
We address the long-standing problem of the existence of a Riemannian metric on \(S^2\times T^2\) with strictly positive biorthogonal curvature (\( K_{\text{biort}}(σ) > 0 \)). Thi…