{"paper":{"title":"Gradient shrinking Ricci solitons of half harmonic Weyl curvature","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Jia-Yong Wu, Peng Wu, William Wylie","submitted_at":"2014-10-27T16:47:03Z","abstract_excerpt":"We prove that a four-dimensional gradient shrinking Ricci soliton with $\\delta W^{\\pm}=0$ is either Einstein, or a finite quotient of $S^3\\times\\mathbb{R}$, $S^2\\times\\mathbb{R}^2$ or $\\mathbb{R}^4$. We also prove that a four-dimensional cscK gradient Ricci soliton is either K\\\"ahler-Einstein, or a finite quotient of $M\\times\\mathbb{C}$, where $M$ is a Riemann surface. The main arguments are curvature decompositions, the Weitzenb\\\"ock formula for half Weyl curvature, and the maximum principle."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.7303","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":""},"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"}