{"paper":{"title":"A Restricted Chen-Nagano Variational Principle for the Einstein-Hilbert Functional","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Irina Tsyganok, Sergey Stepanov","submitted_at":"2026-06-09T11:05:06Z","abstract_excerpt":"This paper introduces a restricted Chen-Nagano variational principle for the Einstein-Hilbert functional on compact Riemannian manifolds. Instead of considering arbitrary symmetric variations of the metric, we restrict the variational problem to an infinite-dimensional subspace determined by the Chen-Nagano gauge constraint. We derive the corresponding restricted Euler-Lagrange equations and obtain a novel structural characterization of critical metrics. The resulting criticality condition is expressed by the equation $E_g = B_g^{*}(\\theta) + c\\,g$ which may be regarded as a restricted counter"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.10704","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.10704/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}