{"paper":{"title":"Codazzi Tensors with Two Eigenvalue Functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Gabe Merton","submitted_at":"2011-11-29T21:57:49Z","abstract_excerpt":"This paper addresses a gap in the classifcation of Codazzi tensors with exactly two eigenfunctions on a Riemannian manifold of dimension three or higher. Derdzinski proved that if the trace of such a tensor is constant and the dimension of one of the the eigenspaces is $n-1$, then the metric is a warped product where the base is an open interval- a conclusion we will show to be true under a milder trace condition. Furthermore, we construct examples of Codazzi tensors having two eigenvalue functions, one of which has eigenspace dimension $n-1$, where the metric is not a warped product with inte"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.7002","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"}