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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"},"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":"1503.04279","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-03-14T07:44:52Z","cross_cats_sorted":[],"title_canon_sha256":"6b00d9d993e376af7c021f653adf388bf12852ad25ed61b872916e4a31adbf7e","abstract_canon_sha256":"d134f5165a25d57c420d53a637c2c7fc4a62e02f5330a82a1d3aa2ca2e01523f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:26:02.853800Z","signature_b64":"ueOM5CW5+ajtqskfplMZPhOr6b47uCRh9y9haP1QdzzXt7KWZevYu7/pPitwRosiSV/LbqHf175aTvkQlPU+Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9a0d787f30b803fd41df2ce791199590451fa28d82095a3f301be62e463a96c9","last_reissued_at":"2026-05-18T01:26:02.853306Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:26:02.853306Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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. 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