{"paper":{"title":"On submaximal dimension of the group of almost isometries of Finsler metrics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.DG","authors_text":"Vladimir S. Matveev","submitted_at":"2012-07-30T12:54:08Z","abstract_excerpt":"We show that the second greatest possible dimension of the group of (local) almost isometries of a Finsler metric is $\\frac{n^2 -n}{2} +1$ for $n= dim(M)\\ne 4 $ and $\\frac{n^2 -n}{2} +2 =8$ for $n=4$. If a Finsler metric has the group of almost isometries of dimension greater than $\\frac{n^2 -n}{2} +1$, then the Finsler metric is Randers, i.e., $F(x,y)= \\sqrt{g_x(y,y)} + \\tau(y)$. Moreover, if $n\\ne 4$, the Riemannian metric $g$ has constant sectional curvature and, if in addition $n\\ne 2$, the 1-form $\\tau$ is closed, so (locally) the metric admits the group of local isometries of the maximal"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.6922","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"}