{"paper":{"title":"Third order Einstein deformations for Kaehler-Einstein metrics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Paul-Andi Nagy","submitted_at":"2026-06-03T06:32:32Z","abstract_excerpt":"For compact K\\\"ahler manifolds $(M,g,J)$ with negative scalar curvature we study the existence problem for non-trivial Einstein deformations of $g$, that is small time curves $g_t$ of Einstein metrics with $g_0=g$. No asssumption on the complex structure $J$ is made; also we do not assume that the metrics $g_t$ are K\\\"ahler w.r.t. $J$. We determine explicitly the obstruction to third order Einstein deformation for $g$; that is we fully solve the equations $(\\Ric^{g_t})^{(k)}(0)=0$ for $1 \\leq k \\le 3$ in terms of the Taylor expansion $g^{-1}g_t=\\id+th_1+\\tfrac{t^2}{2!}h_2+\\tfrac{t^3}{3!}h_3+o("},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.04501","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/2606.04501/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"}