{"paper":{"title":"Harmonic Mappings into non-negatively curved Riemannian manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Irina Tsyganok, Sergey Stepanov","submitted_at":"2015-08-26T09:23:53Z","abstract_excerpt":"Fifty years ago, Eells and Sampson have proved a famous theorem in which they argued that any harmonic mapping $f:(M,g) \\rightarrow (\\bar{M},\\bar{g})$ is totally geodesic if $(M, g)$ is a compact manifold with the nonnegative Ricci tensor and the section curvature of $(\\bar{M},\\bar{g})$ is nonpositive. Moreover, other main results of the theory of harmonic mappings \"in the large\" are the results on harmonic maps into nonpositively curved Riemannian manifolds.\n  In our paper we develop a theory of harmonic mappings into Riemannian manifolds with nonnegative sectional curvature. In particular, w"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.06418","kind":"arxiv","version":3},"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"}