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We show that $m$ is even, say $m = 2k$, and any such hypersurface becomes an open part of a tube around a $k$-dimensional complex hyperbolic space ${\\mathbb C}H^k$ which is embedded canonically in ${Q^*}^{2k}$ as a totally geodesic complex submanifold or a horosphere whose center at infinity is $\\frak A$-isotropic singular. As a consequence of the result, we get the non-existence of real hypersurfaces with isometric Reeb flow in odd-dimensional complex qua"},"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":"1608.02290","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-08-08T01:05:33Z","cross_cats_sorted":[],"title_canon_sha256":"9c7288265aa46b57f8cdef7795ba54be57e2d135e7ba4da1c47c97b18037fb29","abstract_canon_sha256":"24d41d5f0a217f6ffab4e419c56660d5922f7e9183610af636b98c9f8e599bd8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:09:40.563587Z","signature_b64":"AnzXJoyJpNBYWnRAoWHwIlpXNE8IbZY+JyYx8UjsISPjj0OFnwDhvFQkom6Iy/hau5H3LBDIdV2po8bHIqpWAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"618c3d37e771911c32966abb2250c159a46d39b6739f39150f1055954264197c","last_reissued_at":"2026-05-18T01:09:40.563053Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:09:40.563053Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Isometric Reeb flow in complex hyperbolic quadrics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Young Jin Suh","submitted_at":"2016-08-08T01:05:33Z","abstract_excerpt":"We classify real hypersurfaces with isometric Reeb flow in the complex hyperbolic quadrics ${Q^*}^{m} = SO^{o}_{2,m}/SO_mSO_2$, $m \\geq 3$. 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