{"paper":{"title":"Surfaces in $mathbb{R}^4$ with constant principal angles with respect to a plane","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Antonio J. Di Scala, Gabriel Ruiz-Hernandez, Osvaldo Osuna-Castro, Pierre Bayard","submitted_at":"2011-05-09T20:32:42Z","abstract_excerpt":"We study surfaces in $\\R^4$ whose tangent spaces have constant principal angles with respect to a plane. Using a PDE we prove the existence of surfaces with arbitrary constant principal angles. The existence of such surfaces turns out to be equivalent to the existence of a special local symplectomorphism of $\\R^2$. We classify all surfaces with one principal angle equal to 0 and observe that they can be constructed as the union of normal holonomy tubes. We also classify the complete constant angles surfaces in $\\R^4$ with respect to a plane. They turn out to be extrinsic products. We character"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.1791","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":""},"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"}