{"paper":{"title":"On $3$-dimensional $\\left(\\varepsilon \\right)$-para Sasakian manifold","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Punam Gupta","submitted_at":"2014-03-20T10:35:29Z","abstract_excerpt":"The purpose of the present paper is to study the globally and locally $\\varphi $-${\\cal T}$-symmetric $\\left( \\varepsilon \\right) $-para Sasakian manifold in dimension $3$. The globally $\\varphi $-$ {\\cal T}$-symmetric $3$-dimensional $\\left( \\varepsilon \\right) $-para Sasakian manifold is either Einstein manifold or has a constant scalar curvature. The necessary and sufficient condition for Einstein manifold to be globally $\\varphi $-${\\cal T}$ -symmetric is given. A $3$-dimensional $% \\left( \\varepsilon \\right) $ -para Sasakian manifold is locally $\\varphi $-$ {\\cal T}$-symmetric if and only"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.5090","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"}