{"paper":{"title":"Sub-Randers metrics","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Layth M. Alabdulsada","submitted_at":"2026-06-20T07:38:43Z","abstract_excerpt":"We introduce a new class of sub-Finsler metrics, called sub-Randers metrics, obtained by adding a one-form $\\beta \\in \\Gamma(\\mathcal{D}^*)$ to a sub-Riemannian metric $a$ on a bracket-generating distribution $\\mathcal{D} \\subseteq TM$. We define a sub-Randers manifold as a triple $(M, \\mathcal{D}, F)$, where $M$ is an $n$-dimensional smooth manifold and $F(v) = \\sqrt{a(v,v)} + \\beta(v)$, the condition $\\|\\beta\\|_a < 1$ ensures positive definiteness and convexity. Explicit equations for sub-Randers normal geodesics are derived via the Pontryagin Maximum Principle, and we show that normal geode"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.21922","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.21922/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"}