{"id":"W2032094479","doi":"10.1142/s0129167x01001052","title":"A SPLITTING THEOREM FOR KÄHLER MANIFOLDS WHOSE RICCI TENSORS HAVE CONSTANT EIGENVALUES","year":2001,"lang":"en","type":"article","venue":"International Journal of Mathematics","topic":"Geometry and complex manifolds","field":"Mathematics","cited_by":62,"is_retracted":false,"has_abstract":true,"ca_institutions":"Université du Québec à Montréal","funders":"","keywords":"Mathematics; Eigenvalues and eigenvectors; Dimension (graph theory); Conjecture; Pure mathematics; Constant (computer programming); Manifold (fluid mechanics); Ricci curvature; Mathematical analysis; Zero (linguistics); Holonomy; Homogeneous; Complex dimension; Tensor (intrinsic definition); Kähler manifold; Combinatorics; Geometry; Physics; Quantum mechanics; Curvature","routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0005851358,0.0006515187,0.0004885624,0.001918742,0.001002223,0.0009265905,0.000491333,0.0006412263,0.003272743],"category_scores_gemma":[0.00126072,0.0002905387,0.0005793938,0.0004938617,0.001992552,0.001813903,0.00168215,0.0009575918,0.0006591829],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.000672014,"about_ca_system_score_gemma":0.0002786285,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0003180268,"about_ca_topic_score_gemma":0.0002023184,"domain_scores_codex":[0.9997513,0.0000406314,0.00001785034,0.00006645046,0.00008583433,0.0000380135],"domain_scores_gemma":[0.9993784,0.0001389812,0.000110436,0.00009482284,0.0001378191,0.0001394684],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.00002793392,0.00001409205,0.0009543038,0.00009727754,0.00002443071,0.0002931888,0.0005059229,0.001640208,0.007383187,0.9744674,0.001894287,0.01269778],"study_design_scores_gemma":[0.00002120163,0.00005961748,0.001421803,0.00003749159,0.00001950364,0.001082606,0.0001609529,0.0156287,0.003003893,0.9683483,0.01019175,0.00002424745],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.5704511,0.004028922,0.3121417,0.001395496,0.0003947374,0.0001171605,0.0003961161,0.0004528696,0.1106218],"genre_scores_gemma":[0.9511133,0.0006645855,0.03460893,0.0002820254,0.0002185111,0.00007731713,0.0003324308,0.00008605138,0.01261684],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.003272743,"threshold_uncertainty_score":0.01094842,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.07531293277693447,"score_gpt":0.3486827392419615,"score_spread":0.2733698064650271,"validation_status":"score_only:v0-immature-baseline","note":"Baseline scores from an immature model (maturity gate not passed). Scores rank; they never assert a category."}}