{"paper":{"title":"Volumes and geodesic ball packings to the regular prism tilings in $\\widetilde{\\mathbf{S}\\mathbf{L}_2\\mathbf{R}}$ space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.MG","authors_text":"Emil Moln\\'ar, Jen\\\"o Szirmai","submitted_at":"2013-04-02T07:25:04Z","abstract_excerpt":"After having investigated the regular prisms and prism tilings in the $\\SLR$ space in the previous work \\cite{Sz13-1} of the second author, we consider the problem of geodesic ball packings related to those tilings and their symmetry groups $\\mathbf{pq2_1}$. $\\SLR$ is one of the eight Thurston geometries that can be derived from the 3-dimensional Lie group of all $2\\times 2$ real matrices with determinant one.\n  In this paper we consider geodesic spheres and balls in $\\SLR$ (even in $\\mathbf{SL_{\\mathrm{2}}R})$, if their radii $\\rho\\in [0, \\frac{\\pi}{2})$, and determine their volumes. Moreover"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.0546","kind":"arxiv","version":2},"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"}