{"id":"W1910494600","doi":"10.1090/s0002-9947-02-03132-x","title":"Some properties of the Schouten tensor and applications to conformal geometry","year":2002,"lang":"en","type":"article","venue":"Transactions of the American Mathematical Society","topic":"Geometric Analysis and Curvature Flows","field":"Mathematics","cited_by":106,"is_retracted":false,"has_abstract":true,"ca_institutions":"McMaster University","funders":"Natural Sciences and Engineering Research Council of Canada; National Science Foundation","keywords":"Mathematics; Riemann curvature tensor; Weyl tensor; Ricci decomposition; Ricci curvature; Curvature of Riemannian manifolds; Invariant (physics); Conformal map; Curvature; Pure mathematics; Tensor (intrinsic definition); Tensor density; Mathematical physics; Conformal geometry; Eigenvalues and eigenvectors; Mathematical analysis; Scalar curvature; Tensor field; Geometry; Exact solutions in general relativity; Conformal field theory; Sectional curvature; Physics; Quantum mechanics","routes":{"ca_aff":true,"ca_fund":true,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0002571614,0.0001376133,0.0004369489,0.00004590811,0.0002181146,0.00002078018,0.0004620386,0.00004547606,0.0001165452],"category_scores_gemma":[0.0001312303,0.00006994973,0.0004852776,0.001349835,0.0006426313,0.00008889798,0.00004868784,0.0002129877,0.00001012869],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00002321867,"about_ca_system_score_gemma":0.00001448849,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00002077851,"about_ca_topic_score_gemma":0.000002172959,"domain_scores_codex":[0.9987862,0.00004237111,0.0004251856,0.000146013,0.0004116845,0.000188554],"domain_scores_gemma":[0.9987345,0.0001978398,0.0002764674,0.0006050331,0.0001125118,0.00007359879],"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":[0.0002556169,0.01528275,0.005853678,0.01139747,0.01142954,6.459077e-7,0.06307274,0.003277034,0.08209814,0.6140128,0.03243195,0.1608877],"study_design_scores_gemma":[0.006749798,0.002389767,0.0437681,0.002790041,0.01568843,0.0002550631,0.1170074,0.1009095,0.118415,0.5538313,0.03274997,0.005445669],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8767515,0.0003604128,0.1155723,0.005162398,0.00004297125,0.001218689,0.00004807106,0.00006105326,0.0007825249],"genre_scores_gemma":[0.986722,0.00005617809,0.01166113,0.0002837113,0.00003100057,0.00007635657,9.224722e-8,0.00001559591,0.001153925],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.155442,"threshold_uncertainty_score":0.2852467,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03304259906961583,"score_gpt":0.2572522435634311,"score_spread":0.2242096444938153,"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."}}