{"paper":{"title":"The Spin$^c$ Dirac Operator on Hypersurfaces and Applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Julien Roth, Roger Nakad","submitted_at":"2012-07-12T08:39:24Z","abstract_excerpt":"We extend to the eigenvalues of the hypersurface Spin$^c$ Dirac operator well known lower and upper bounds. Examples of limiting cases are then given. Futhermore, we prove a correspondence between the existence of a Spin$^c$ Killing spinor on homogeneous 3-dimensional manifolds $\\mathbb E^*(\\kappa, \\tau)$ with 4-dimensional isometry group and isometric immersions of $\\mathbb E^*(\\kappa, \\tau)$ into the complex space form $\\mathbb M^4(c)$ of constant holomorphic sectional curvature $4c$, for some $c\\in \\mathbb R^*$. As applications, we show the non-existence of totally umbilic surfaces in $\\mat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.2877","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"}