{"paper":{"title":"Generalization of two Bonnet's Theorems to the relative Differential Geometry of the 3-dimensional Euclidean space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Ioannis Delivos, Ioannis Kaffas, Stylianos Stamatakis","submitted_at":"2017-01-29T10:13:42Z","abstract_excerpt":"This paper is devoted to the 3-dimensional relative differential geometry of surfaces. In the Euclidean space $\\R{E} ^3 $ we consider a surface $\\varPhi %\\colon \\vect{x} = \\vect{x}(u^1,u^2) $ with position vector field $\\vect{x}$, which is relatively normalized by a relative normalization $\\vect{y}% (u^1,u^2) $. A surface $\\varPhi^*% \\colon \\vect{x}^* = \\vect{x}^*(u^1,u^2) $ with position vector field $\\vect{x}^* = \\vect{x} + \\mu \\, \\vect{y}$, where $\\mu$ is a real constant, is called a relatively parallel surface to $\\varPhi$. Then $\\vect{y}$ is also a relative normalization of $\\varPhi^*$. T"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.09086","kind":"arxiv","version":3},"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"}