{"paper":{"title":"Killing Symmetry on Finsler Manifold","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"gr-qc","authors_text":"Muneyuki Ishida, Ryoko Yahagi, Takayoshi Ootsuka","submitted_at":"2016-09-09T07:51:27Z","abstract_excerpt":"Killing vector fields $K$ are defined on Finsler manifold. The Killing symmetry is reformulated simply as $\\delta K^\\flat =0$ by using the Killing non-linear 1-form $K^\\flat$ and the spray operator $\\delta$ with the Finsler non-linear connection. $K^\\flat$ is related to the generalization of Killing tensors on Finsler manifold, and the condition $\\delta K^\\flat =0$ gives an analytical method of finding higher derivative conserved quantities, which may be called hidden conserved quantities. We show two examples: the Carter constant on Kerr spacetime and the Runge-Lentz vectors in Newtonian grav"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.02677","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"}