{"paper":{"title":"On the Tchebychev Vector Field in the Relative Differential Geometry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Stylianos Stamatakis","submitted_at":"2015-11-29T21:01:56Z","abstract_excerpt":"In this paper we deal with relative normalizations of hypersurfaces in the (n+1)-dimensional Euclidean space $\\mathbb{R}^{n+1}$. Considering a relative normalization $\\bar{y}$ of an hypersurface $\\Phi$ we decompose the corresponding Tchebychev vector $\\bar{T}$ in two components, one parallel to the Tchebychev vector $\\bar{T}_{EUK}$ of the Euclidean normalization $\\bar{\\xi}$ and one parallel to the orthogonal projection $\\bar{y}_{T}$ of $\\bar{y}$ in the tangent hyperplane of $\\Phi$. We use this decomposition to investigate some properties of $\\Phi$, which concern its Gaussian curvature, the sup"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.00405","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"}