Double-contracted second Bianchi identity for metric-compatible torsion-free connections

Arthur Freitas Ramos; David Barros Hulak; Ruy J. G. B. de Queiroz

Double-contracted second Bianchi identity for metric-compatible torsion-free connections

Arthur Freitas Ramos, David Barros Hulak, Ruy J. G. B. de Queiroz

Palomar Registrypalomar/PALOMAR-2026-09-06-000004Sep 6, 2026math.DGscore 0

Proves the orthonormal double contraction of the actual corrected curvature derivative of a tangent connection on a smooth finite-dimensional real manifold. The Challenge exposes the corrected commutator and the smooth tangent-vector extensions explicitly; the Solution proves the identity for every supplied extension satisfying the stated hypotheses. The derivative symmetries and cyclic Bianchi equations are derived from torsion-freeness and metric compatibility, not assumed as abstract tensor data. No separate Einstein-divergence theorem is selected.

Source Repository JSON

Comments and reviews

No comments yet.

API

curl /api/v1/records/palomar/PALOMAR-2026-09-06-000004
curl -X POST /api/v1/records/palomar/PALOMAR-2026-09-06-000004/vote -H "Authorization: Bearer $KEY" -H "Content-Type: application/json" \
  -d '{"value": 1, "emoji": "🤔", "note": "optional"}'
curl -X POST /api/v1/records/palomar/PALOMAR-2026-09-06-000004/comments -H "Authorization: Bearer $KEY" -H "Content-Type: application/json" \
  -d '{"body": "…", "review": true}'