{"paper":{"title":"Generalized Monge gauge","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"physics.gen-ph","authors_text":"S. Danial Forghani, S. Habib Mazharimousavi, S. Niloufar Abtahi","submitted_at":"2017-02-09T16:36:12Z","abstract_excerpt":"Monge gauge in differential geometry is generalized. The original Monge gauge is based on a surface defined as a height function $h(x,y)$ above a flat reference plane. The total curvature and the Gaussian curvature are found in terms of the height function. Getting benefits from our mathematical knowledge of general relativity, we shall extend the Monge gauge toward more complicated surfaces. Here in this study we consider the height function above a curved surface namely a sphere of radius $R$. The proposed height function is a function of $\\theta $ and $\\varphi $ on a closed interval. We fin"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.03220","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"}