{"paper":{"title":"The geometry of Gauss map and shape operator in simply isotropic and pseudo-isotropic spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Luiz C. B. da Silva","submitted_at":"2018-01-03T21:43:27Z","abstract_excerpt":"In this work, we are interested in the differential geometry of surfaces in simply isotropic $\\mathbb{I}^3$ and pseudo-isotropic $\\mathbb{I}_{\\mathrm{p}}^3$ spaces, which consists of the study of $\\mathbb{R}^3$ equipped with a degenerate metric such as $\\mathrm{d}s^2=\\mathrm{d}x^2\\pm\\mathrm{d}y^2$. The investigation is based on previous results in the simply isotropic space [B. Pavkovi\\'c, Glas. Mat. Ser. III $\\mathbf{15}$, 149 (1980); Rad JAZU $\\mathbf{450}$, 129 (1990)], which point to the possibility of introducing an isotropic Gauss map taking values on a unit sphere of parabolic type and "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.01187","kind":"arxiv","version":4},"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"}