{"paper":{"title":"A Study of Three-Dimensional Paracontact $(\\kappa ,\\mu ,\\nu) $-SPACES","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Cengizhan Murathan, Irem Kupeli Erken","submitted_at":"2013-05-07T13:47:54Z","abstract_excerpt":"This paper is a study of three-dimensional paracontact metric (\\k{appa},{\\mu},{\\nu})-manifolds. Three dimensional paracontact metric manifolds whose Reeb vector field {\\xi} is harmonic are characterized. We focus on some curvature properties by considering the class of paracontact metric (\\k{appa},{\\mu},{\\nu})-manifolds under a condition which is given at Definition 3.1. We study properties of such manifolds according to the cases \\k{appa}>-1, \\k{appa}=-1, \\k{appa}<-1 and construct new examples of such manifolds for each case."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.1511","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"}