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Then $p$ is an $\\textit{isotropic point}$ if there exists a constant $\\kappa_p \\in \\mathbf{R}$ such that $\\mathcal{J}_v = \\kappa_p \\textit{ Id}_{v^\\perp}$ for each unit vector $v \\in T_pM$. If all points are isotropic, then $M$ is said to be isotropic; it is a classical result of Schur that isotropic manifolds of dimension at least 3 have constant sectional cu"},"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":"1808.02475","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-08-07T17:51:51Z","cross_cats_sorted":[],"title_canon_sha256":"d007d7625a576d47df5fa723ef3de6ea75be014b68c8ed024841f099e524d06d","abstract_canon_sha256":"d5e48f36931630e20814c46da439c26a0cbb366d75e1b26a3e03c88f9ac8472a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:08:36.963414Z","signature_b64":"ip4SglmBl2otpHs6sX2EEPbNzC7WNeZ8grq/TIZHvcmRnZJq8xu2EqX8cDZDt6+bi8DxlIc9n3yzVRyoVNsoBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"97b7c2ec37190c3acc8f0ca5f4556beea851289284f6f61c4f1f7a86f697b3b7","last_reissued_at":"2026-05-18T00:08:36.962890Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:08:36.962890Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Almost Isotropic Kaehler Manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Benjamin Schmidt, Krishnan Shankar, Ralf Spatzier","submitted_at":"2018-08-07T17:51:51Z","abstract_excerpt":"Let $M$ be a complete Riemannian manifold and suppose $p\\in M$. 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