{"paper":{"title":"Hermitian symmetric space, flat bundle and holomorphicity criterion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.DG","authors_text":"C. S. Rajan, Hassan Azad, Indranil Biswas, Shehryar Sikander","submitted_at":"2016-03-08T05:40:36Z","abstract_excerpt":"Let $K\\backslash G$ be an irreducible Hermitian symmetric space of noncompact type and $\\Gamma \\,\\subset\\, G$ a closed torsionfree discrete subgroup. Let $X$ be a compact K\\\"ahler manifold and $\\rho\\, :\\, \\pi_1(X, x_0)\\,\\longrightarrow\\, \\Gamma$ a homomorphism such that the adjoint action of $\\rho(\\pi_1(X, x_0))$ on $\\text{Lie}(G)$ is completely reducible. A theorem of Corlette associates to $\\rho$ a harmonic map $X\\, \\longrightarrow\\, K\\backslash G/\\Gamma$. We give a criterion for this harmonic map to be holomorphic. We also give a criterion for it to be anti--holomorphic."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.02387","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"}