{"paper":{"title":"Almost para-Hermitian and almost paracontact metric structures induced by natural Riemann extensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Cornelia-Livia Bejan, Galia Nakova","submitted_at":"2018-03-25T08:29:57Z","abstract_excerpt":"In this paper we consider a manifold $(M,\\nabla )$ with a symmetric linear connection $\\nabla $ which induces on the cotangent bundle $T^*M$ of $M$ a semi-Riemannian metric $\\overline g$ with a neutral signature. The metric $\\overline g$ is called natural Riemann extension and it is a generalization (made by M. Sekizawa and O. Kowalski) of the Riemann extension, introduced by E. K. Patterson and A. G. Walker (1952). We construct two almost para-Hermitian structures on $(T^*M,\\overline g)$ which are almost para-K\\\"ahler or para-K\\\"ahler and prove that the defined almost para-complex structures "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.09213","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"}