{"paper":{"title":"Bach flows of product manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"gr-qc","authors_text":"Sanjit Das, Sayan Kar","submitted_at":"2010-12-20T06:23:25Z","abstract_excerpt":"We investigate various aspects of a geometric flow defined using the Bach tensor. Firstly, using a well-known split of the Bach tensor components for $(2,2)$ unwarped product manifolds, we solve the Bach flow equations for typical examples of product manifolds like $S^2\\times S^2$, $R^2\\times S^2$. In addition, we obtain the fixed point condition for general $(2,2)$ manifolds and solve it for a restricted case. Next, we consider warped manifolds. For Bach flows on a special class of asymmetrically warped four manifolds, we reduce the flow equations to a first order dynamical system, which is s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.4244","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"}