{"paper":{"title":"Two-step homogeneous geodesics in homogeneous 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":"2016-11-14T10:38:16Z","abstract_excerpt":"We study geodesics of the form $\\gamma(t)=\\pi(\\exp(tX)\\exp(tY))$, $X,Y\\in \\fr{g}=\\operatorname{Lie}(G)$, in homogeneous spaces $G/K$, where $\\pi:G\\rightarrow G/K$ is the natural projection. These curves naturally generalise homogeneous geodesics, that is orbits of one-parameter subgroups of $G$ (i.e. $\\gamma(t)=\\pi(\\exp (tX))$, $X\\in \\fr{g}$). We obtain sufficient conditions on a homogeneous space implying the existence of such geodesics for $X,Y\\in \\fr{m}=T_o(G/K)$. We use these conditions to obtain examples of Riemannian homogeneous spaces $G/K$ so that all geodesics of $G/K$ are of the abov"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.04325","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"}