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We define a left invariant Riemannian metric on $N$ compatible with $J$ to be minimal, if it minimizes the norm of the invariant part of the Ricci tensor among all compatible metrics with the same scalar curvature. In [L1], J. Lauret proved that minimal metrics (if any) are unique up to isometry and scaling. This uniqueness allows us to distinguish two complex structures with Riemannian data, giving rise to a great deal of invariants.\n  We show how to use a Riemannian invariant:"},"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":"1302.6543","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-02-26T19:15:30Z","cross_cats_sorted":["math.SG"],"title_canon_sha256":"ad731b409c232831d098dbd2f31862f2d0cbc247034cf2b41b3370bda698732e","abstract_canon_sha256":"5c12922f8f26282bf5213f6d2e1aaf77959d90c3602b9c29a3f78b543de718fa"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:30:40.806932Z","signature_b64":"qRv/Q3rPzNkt9H1S+Hp/EUXZC5nvHeuvlfGM5szhd6JPbGCnWm28vsEen9cV3RG86DijuT3uuelamIaN86/KAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9aad9bb4bb24ee2b8b0655ccca8f4ac5b711905159511d4a139dfc44db0df465","last_reissued_at":"2026-05-18T03:30:40.806105Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:30:40.806105Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Invariants of complex structures on nilmanifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SG"],"primary_cat":"math.DG","authors_text":"Edwin Alejandro Rodriguez Valencia","submitted_at":"2013-02-26T19:15:30Z","abstract_excerpt":"Let $(N, J)$ be a simply connected $2n$-dimensional nilpotent Lie group endowed with an invariant complex structure. 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