{"paper":{"title":"On the shape operator of relatively parallel hypersurfaces in the $n$-dimensional relative differential geometry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Ioannis Kaffas, Stylianos Stamatakis","submitted_at":"2017-12-28T10:02:52Z","abstract_excerpt":"We deal with hypersurfaces in the framework of the $n$-dimensional relative differential geometry.  We consider a hypersurface $\\varPhi$ of $\\mathbb{R}^{n+1}$ with position vector field $\\mathbf{x}$, which is relatively normalized by a relative normalization $\\mathbf{y}$. Then $\\mathbf{y}$ is also a relative normalization of every member of the one-parameter family $\\mathcal{F}$ of hypersurfaces $\\varPhi_\\mu$ with position vector field $$\\mathbf{x}_\\mu = \\mathbf{x} + \\mu \\, \\mathbf{y},$$ where $\\mu$ is a real constant. We call every hypersurface $\\varPhi_\\mu \\in \\mathcal{F}$ relatively paralle"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.10319","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"}