{"paper":{"title":"Concurrent $\\pi$-vector fields and energy beta-change","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["gr-qc","math-ph","math.MP"],"primary_cat":"math.DG","authors_text":"A. Soleiman, Nabil L. Youssef, S. H. Abed","submitted_at":"2008-05-16T18:43:05Z","abstract_excerpt":"The present paper deals with an \\emph{intrinsic} investigation of the notion of a concurrent $\\pi$-vector field on the pullback bundle of a Finsler manifold $(M,L)$. The effect of the existence of a concurrent $\\pi$-vector field on some important special Finsler spaces is studied. An intrinsic investigation of a particular $\\beta$-change, namely the energy $\\beta$-change ($\\widetilde{L}^{2}(x,y)=L^{2}(x,y)+ B^{2}(x,y) with \\ B:=g(\\bar{\\zeta},\\bar{\\eta})$; $\\bar{\\zeta} $ being a concurrent $\\pi$-vector field), is established. The relation between the two Barthel connections $\\Gamma$ and $\\widet"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0805.2599","kind":"arxiv","version":3},"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"}