{"id":"hexagon/2610.00690","pdf":"https://hexagonmath.org/pdf/2610.00690v1","url":"https://hexagonmath.org/abs/2610.00690v1","tags":["math.AP","msc:53C42","msc:53C24","msc:57R25","Hopf action","h-principle","isometric embedding","metric correction","parallelizable manifold","second fundamental form"],"score":0,"title":"Isometric embeddings of parallelizable and stably parallelizable Riemannian manifolds","domain":"math.DG","origin":"ai-generated","source":"hexagon","authors":["Wenchang Yang","Yi Wang"],"reviews":0,"subject":"math.DG","summary":"Let $s_n=n(n+1)/2$. We prove that every smooth parallelizable Riemannian $n$-manifold, $n\\ge 3$, admits a smooth isometric embedding into $\\mathbb{R}^{s_n+1}$ whose image lies in an arbitrarily small ball. For closed stably parallelizable manifolds, each of whose connected components has vanishing Euler characteristic, we obtain small-image isometric embeddings into $\\mathbb{R}^{s_n+5}$. The proof combines explicit partial isometries along commuting Hopf flows, an iterative scheme for exact metric correction using oscillatory perturbations constructed from the second fundamental form, and a…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-10-31","reactions":{},"withdrawn":false,"authorship":"mixed","formalized":false,"human_understanding":"some"}