{"paper":{"title":"Sub-Riemannian geodesics on the free Carnot group with the growth vector (2,3,5,8)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.OC","authors_text":"Yuri Sachkov","submitted_at":"2014-04-30T14:59:28Z","abstract_excerpt":"We consider the free nilpotent Lie algebra $L$ with 2 generators, of step 4, and the corresponding connected simply connected Lie group $G$. We study the left-invariant sub-Riemannian structure on $G$ defined by the generators of $L$ as an orthonormal frame.\n  We compute two vector field models of $L$ by polynomial vector fields in $R^8$, and find an infinitesimal symmetry of the sub-Riemannian structure. Further, we compute explicitly the product rule in $G$, the right-invariant frame on $G$, linear on fibers Hamiltonians corresponding to the left-invariant and right-invariant frames on $G$, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.7752","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"}