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Assuming additionally that $G$ acts completely reducible on $\\mathbb R^{n+1}$, we also obtain that any $G$-homogeneous Einstein pseudo-Riemannian metric on a real, complex or quaternionic pseudo-hyperbolic space, or on a para-complex or para-quaternionic projective space is homothetic t"},"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":"1309.1390","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-09-05T16:14:32Z","cross_cats_sorted":[],"title_canon_sha256":"b185aa96e2655a28d8ad55d11ae81d0b8cc53092cbe6d233b0e6064e1aaa01cd","abstract_canon_sha256":"599d9d9247837794c68d2815db072c2766b6ffbb9fb76be65979f24858bf287d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:20:40.373582Z","signature_b64":"4AmJFi+20GzQwyrR599xM6fN4QfZM4jcEM6dzldT60hYB5hJkIiu9Atdczfa+L3I0Ba31CFkcfGCkOp6wmZbBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3c0372227bd1e91aae83e37a414511fe73e5fefccb1f00a143dfcbff51a3bd96","last_reissued_at":"2026-05-18T00:20:40.372854Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:20:40.372854Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Classification of homogeneous Einstein metrics on pseudo-hyperbolic spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Gabriel Baditoiu","submitted_at":"2013-09-05T16:14:32Z","abstract_excerpt":"We classify the effective and transitive actions of a Lie group $G$ on an n-dimensional non-degenerate hyperboloid (also called real pseudo-hyperbolic space), under the assumption that $G$ is a closed, connected Lie subgroup of $SO_0(n-r,r+1)$, the connected component of the indefinite special orthogonal group. 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