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This manifold is diffeomorphic to the homogeneous space $\\SO(n)/\\SO(n-q)$ and its isotropy representation contains equivalent summands. %This causes difficulty in the description of all $\\SO(n)$-invariant metrics.\n  We prove, by assuming additional symmetries, that $V_4\\bb{R}^n$ $(n\\ge 6)$ admits at least four $\\SO(n)$-invariant Einstein metrics, two of which are Jensen's metrics and the other two are new metrics. Moreover, we prove that $V_5\\bb{R}^7$ admits at least six i"},"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":"1311.1579","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-11-07T05:25:18Z","cross_cats_sorted":[],"title_canon_sha256":"ff55484efb2d7975b360132c3eb055d50c5ec4734745e511e5ace68f147a05d2","abstract_canon_sha256":"85462aee07d567f187583c4814934805b3f43a1a525761f1035a0763f8af5071"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:26:03.146125Z","signature_b64":"x4/lVGNtofafnvf4aKIPgryAdowyEqy7FZZ89Yox0XCuOMDmfhZn+JluzRIzoaxh+SY0PeW7sCk3s2Vm32OxBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b360f3b0e507fc8cbaee6eff5ac27a2ba6866008c9b5b6bafbeed61388a65e5c","last_reissued_at":"2026-05-18T01:26:03.145548Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:26:03.145548Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"New homogeneous Einstein metrics on Stiefel manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Andreas Arvanitoyeorgos, Marina Statha, Yusuke Sakane","submitted_at":"2013-11-07T05:25:18Z","abstract_excerpt":"We consider invariant Einstein metrics on the Stiefel manifold $V_q\\bb{R} ^n$ of all orthonormal $q$-frames in $\\bb{R}^n$. This manifold is diffeomorphic to the homogeneous space $\\SO(n)/\\SO(n-q)$ and its isotropy representation contains equivalent summands. %This causes difficulty in the description of all $\\SO(n)$-invariant metrics.\n  We prove, by assuming additional symmetries, that $V_4\\bb{R}^n$ $(n\\ge 6)$ admits at least four $\\SO(n)$-invariant Einstein metrics, two of which are Jensen's metrics and the other two are new metrics. 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