{"paper":{"title":"Minimal surfaces in ${\\mathbb{R}}^{4}$ foliated by conic sections and parabolic rotations of holomorphic null curves in ${\\mathbb{C}}^{4}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Hojoo Lee","submitted_at":"2017-02-20T16:15:45Z","abstract_excerpt":"Using the complex parabolic rotations of holomorphic null curves in ${\\mathbb{C}}^{4}$, we transform minimal surfaces in Euclidean space ${\\mathbb{R}}^{3} \\subset {\\mathbb{R}}^{4}$ to a family of degenerate minimal surfaces in Euclidean space ${\\mathbb{R}}^{4}$. Applying our deformation to holomorphic null curves in ${\\mathbb{C}}^{3} \\subset {\\mathbb{C}}^{4}$ induced by helicoids in ${\\mathbb{R}}^{3}$, we discover new minimal surfaces in ${\\mathbb{R}}^{4}$ foliated by conic sections with eccentricity grater than $1$: hyperbolas or straight lines. Applying our deformation to holomorphic null cu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.06047","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"}