{"paper":{"title":"On Einstein Kropina metrics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Xiaoling Zhang, Yi-Bing Shen","submitted_at":"2012-07-09T04:35:23Z","abstract_excerpt":"In this paper, a characteristic condition of Einstein Kropina metrics is given. By the characteristic condition, we prove that a non-Riemannian Kropina metric $F=\\frac{\\alpha^2}{\\beta}$ with constant Killing form $\\beta$ on an n-dimensional manifold $M$, $n\\geq 2$, is an Einstein metric if and only if $\\alpha$ is also an Einstein metric. By using the navigation data $(h,W)$, it is proved that an n-dimensional ($n\\geq2$) Kropina metric $F=\\frac{\\alpha^2}{\\beta}$ is Einstein if and only if the Riemannian metric $h$ is Einstein and $W$ is a unit Killing vector field with respect to $h$. Moreover,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.1944","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"}