{"paper":{"title":"Properties of modified Riemannian extensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Ali Cakmak, Aydin GEZER, Lokman Bilen","submitted_at":"2013-05-20T09:52:43Z","abstract_excerpt":"Let $M$ be an $n-$dimensional differentiable manifold with a symmetric connection $\\nabla $ and $T^{\\ast}M$ be its cotangent bundle. In this paper, we study some properties of the modified Riemannian extension $% \\widetilde{g}_{\\nabla,c}$ on $T^{\\ast}M$ defined by means of a symmetric $% (0,2)$-tensor field $c$ on $M.$ We get the conditions under which $T^{\\ast}M $ endowed with the horizontal lift $^{H}J$ of an almost complex structure $J$ and with the metric $\\widetilde{g}_{\\nabla,c}$ is a K\\\"{a}hler-Norden manifold. Also curvature properties of the Levi-Civita connection and another metric c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.4478","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"}