{"paper":{"title":"On the Focal Locus of Submanifolds of a Finsler Manifold","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Aritra Bhowmick, Sachchidanand Prasad","submitted_at":"2024-09-04T12:20:19Z","abstract_excerpt":"In this article, we investigate the focal locus of closed (not necessarily compact) submanifolds in a forward complete Finsler manifold. The main goal is to show that the associated normal exponential map is \\emph{regular} in the sense of F.W. Warner (Am. J. of Math., 87, 1965). As a consequence, we show that the normal exponential is non-injective near any tangent focal point. Extending the ideas of Warner, we study the connected components of the regular focal locus. This allows us to identify an open and dense subset, on which the focal time maps are smooth, provided they are finite. We exp"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2409.02643","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2409.02643/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}