{"paper":{"title":"On $(H,\\widetilde{H})$-harmonic Maps between pseudo-Hermitian manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.DG","authors_text":"Yuxin Dong","submitted_at":"2016-10-04T14:55:17Z","abstract_excerpt":"In this paper, we investigate critical maps of the horizontal energy functional $E_{H,\\widetilde{H}}(f)$ for maps between two pseudo-Hermitian manifolds $(M^{2m+1},H(M),J,\\theta )$ and $(N^{2n+1},\\widetilde{H}(N), \\widetilde{J},\\widetilde{\\theta})$. These critical maps are referred to as $(H,\\widetilde{H})$-harmonic maps. We derive a CR Bochner formula for the horizontal energy density $|df_{H, \\widetilde{H}}|^{2}$, and introduce a Paneitz type operator acting on maps to refine the Bochner formula. As a result, we are able to establish some Bochner type theorems for $(H,\\widetilde{H})$-harmoni"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.01032","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"}