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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1611.04325","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-11-14T10:38:16Z","cross_cats_sorted":[],"title_canon_sha256":"94ed696e7ee06838b6aa6f50d9ae48e34484f961357bd99f2042fd7f770a92fb","abstract_canon_sha256":"d83f58676226ffff4d7d162b29b6ca608f8702f5e1bcf2ad440c6a9d8103cd4b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:56:45.066966Z","signature_b64":"NE/kSO+qGvOum/oXw0d+xjrXlnIvggrJ9wlQR0QY6XvfxXlhwm12sc3B5GHQ7rtymAvBz8R+CcGXy2lpaRauBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"855bf83ee9f9660244ff0adcdbcdf7bd2c4c6ec48468a7ae124f2eca77e16f9c","last_reissued_at":"2026-05-18T00:56:45.066356Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:56:45.066356Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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. 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