{"paper":{"title":"Eigenvalue Estimates of the ${\\rm spin}^c$ Dirac Operator and Harmonic Forms on K\\\"ahler-Einstein Manifolds","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Mihaela Pilca, Roger Nakad","submitted_at":"2015-02-18T14:37:23Z","abstract_excerpt":"We establish a lower bound for the eigenvalues of the Dirac operator defined on a compact K\\\"ahler-Einstein manifold of positive scalar curvature and endowed with particular ${\\rm spin}^c$ structures. The limiting case is characterized by the existence of K\\\"ahlerian Killing ${\\rm spin}^c$ spinors in a certain subbundle of the spinor bundle. Moreover, we show that the Clifford multiplication between an effective harmonic form and a K\\\"ahlerian Killing ${\\rm spin}^c$ spinor field vanishes. This extends to the ${\\rm spin}^c$ case the result of A. Moroianu stating that, on a compact K\\\"ahler-Eins"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.05252","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"}