{"paper":{"title":"Kahler-Einstein and Kahler scalar flat supermanifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"John Schulman, J.P. Ang, Martin Rocek","submitted_at":"2016-05-10T23:40:09Z","abstract_excerpt":"Two results regarding K\\\"ahler supermanifolds with potential $K=A+C\\theta\\bar\\theta$ are shown. First, if the supermanifold is K\\\"ahler-Einstein, then its base (the supermanifold of one lower fermionic dimension and with K\\\"ahler potential $A$) has constant scalar curvature. As a corollary, every constant scalar curvature K\\\"ahler supermanifold has a unique superextension to a K\\\"ahler-Einstein supermanifold of one higher fermionic dimension. Second, if the supermanifold is itself scalar flat, then its base satisfies the equation $$ \\phi^{\\bar ji}\\phi_{i\\bar j}=2\\Delta_0 S_0 + R_0^{\\bar ji}R_{"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.03245","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"}