{"paper":{"title":"Maximal Normal Curvature and Veronese Rigidity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Jingbo Wan, Tsz-Kiu Aaron Chow","submitted_at":"2026-07-01T13:48:22Z","abstract_excerpt":"We prove a sharp Veronese rigidity theorem for closed immersed submanifolds of the Euclidean unit ball under intrinsic harmonic-structure assumptions. For an isometric immersion $F:(\\Sigma,g)\\looparrowright\\overline B(1)$, define the maximal normal curvature by \\[\n  \\kappa(F):=\n  \\sup_{x\\in\\Sigma}\n  \\sup_{\\substack{v\\in T_x\\Sigma\\\\ |v|_g=1}}\n  |A_x(v,v)|. \\] If $\\Sigma^{2n}$ is almost Hermitian with harmonic fundamental two-form, or $\\Sigma^{4n}$ is almost quaternion-Hermitian with harmonic fundamental four-form, $n\\ge2$, then \\[\n  \\kappa(F)\\ge \\sqrt{\\frac{2n}{n+1}} . \\] In the equality case t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.00949","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.00949/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}