{"paper":{"title":"Geodesics in generalized Wallach spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Andreas Arvanitoyeorgos, Nikolaos Panagiotis Souris","submitted_at":"2015-03-14T07:44:52Z","abstract_excerpt":"We study geodesics in generalized Wallach spaces which are expressed as orbits of products of three exponential terms. These are homogeneous spaces $M=G/K$ whose isotropy representation decomposes into a direct sum of three submodules $\\frak{m}=\\frak{m}_1\\oplus\\frak{m}_2\\oplus\\frak{m}_3$, satisfying the relations $[\\frak{m}_i,\\frak{m}_i]\\subset \\frak{k}$. Assuming that the submodules $\\frak{m}_i$ are pairwise non isomorphic, we study geodesics on such spaces of the form $\\gamma (t)=\\exp (tX)\\exp (tY)\\exp (tZ)\\cdot o$, where $X\\in\\fr{m}_1, Y\\in\\fr{m}_2, Z\\in\\fr{m}_3$ ($o=eK$), with respect to a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.04279","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"}