{"paper":{"title":"Canonical Coordinates and Principal Directions for Surfaces in $\\H^2\\times\\R$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Ana Irina Nistor, Franki Dillen, Marian Ioan Munteanu","submitted_at":"2009-10-12T11:14:47Z","abstract_excerpt":"In this paper we characterize and classify surfaces in ${\\mathbb{H}}^2\\times{\\mathbb{R}}$ which have a canonical principal direction. Here ${\\mathbb{H}}^2$ denotes the hyperbolic plane. We study some geometric properties such as minimality and flatness. Some examples are given to complete the study."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0910.2135","kind":"arxiv","version":2},"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"}