{"paper":{"title":"Translating solitons in Riemannian products","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Francisco Martin, Jorge H. de Lira","submitted_at":"2018-03-04T20:08:12Z","abstract_excerpt":"In this paper we study solitons invariant with respect to the flow generated by a complete Killing vector field in a ambient Riemannian manifold. A special case occurs when the ambient manifold is the Riemannian product $(\\mathbb{R} \\times P, {\\rm d}t^2+g_0)$ and the Killing field is $X=\\partial_t$. Similarly to what happens in the Euclidean setting, we call them translating solitons. We see that a translating soliton in $\\mathbb{R} \\times P$ can be seen as a minimal submanifold for a weighted volume functional. Moreover we show that this kind of solitons appear in a natural way in the context"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.01410","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"}