{"paper":{"title":"The Energy-Momentum tensor on low dimensional $\\Spinc$ manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Georges Habib, Roger Nakad","submitted_at":"2012-04-02T21:28:11Z","abstract_excerpt":"On a compact surface endowed with any $\\Spinc$ structure, we give a formula involving the Energy-Momentum tensor in terms of geometric quantities. A new proof of a B\\\"{a}r-type inequality for the eigenvalues of the Dirac operator is given. The round sphere $\\mathbb{S}^2$ with its canonical $\\Spinc$ structure satisfies the limiting case. Finally, we give a spinorial characterization of immersed surfaces in $\\mathbb{S}^2\\times \\mathbb{R}$ by solutions of the generalized Killing spinor equation associated with the induced $\\Spinc$ structure on $\\mathbb{S}^2\\times \\mathbb{R}$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.0541","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"}