{"paper":{"title":"A rigidity theorem of $\\xi$-submanifolds in $\\mathbb{C}^{2}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Xingxiao Li, Xiufen Chang","submitted_at":"2015-11-09T05:06:55Z","abstract_excerpt":"In this paper, we first introduce the concept of $\\xi $-submanifold which is a natural generalization of self-shrinkers for the mean curvature flow and also an extension of $\\lambda$-hypersurfaces to the higher codimension. Then, as the main result, we prove a rigidity theorem for Lagrangian $\\xi $-submanifold in the complex $2$-plane $\\bbc^2$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.02568","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"}