{"id":"W2058655323","doi":"10.4153/cmb-2014-063-4","title":"Ricci Curvature Tensor and Non-Riemannian Quantities","year":2014,"lang":"en","type":"article","venue":"Canadian Mathematical Bulletin","topic":"Advanced Differential Geometry Research","field":"Physics and Astronomy","cited_by":32,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Natural Science Foundation of Ningbo; Ningbo University; National Natural Science Foundation of China","keywords":"Ricci curvature; Curvature of Riemannian manifolds; Riemann curvature tensor; Ricci decomposition; Mathematics; Scalar curvature; Weyl tensor; Curvature; Ricci flow; Pure mathematics; Sectional curvature; Curvature form; Metric tensor; Mathematical analysis; Geometry","routes":{"ca_aff":false,"ca_fund":false,"ca_venue":true,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.000837376,0.0009141925,0.0005791989,0.003137674,0.0007847377,0.001883511,0.00056477,0.0009792816,0.005218809],"category_scores_gemma":[0.001705301,0.0002239963,0.0004610621,0.001367081,0.002954478,0.002800505,0.001236154,0.001216276,0.0006326248],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001586891,"about_ca_system_score_gemma":0.0008286147,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00245023,"about_ca_topic_score_gemma":0.001674128,"domain_scores_codex":[0.9992194,0.0001818366,0.00004256392,0.0001290396,0.0003328774,0.00009429594],"domain_scores_gemma":[0.9987663,0.0001910443,0.000291778,0.0001326679,0.0004210456,0.000197227],"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":[0.000009137656,0.000009346778,0.0004427122,0.0000455161,0.000007862485,0.0001459868,0.0001262766,0.001429129,0.00275878,0.9906322,0.001110306,0.00328286],"study_design_scores_gemma":[0.000006700975,0.00004675356,0.004247238,0.0000448999,0.0000189356,0.0004935691,0.0001991518,0.01738369,0.002313616,0.9567354,0.01845832,0.00005167641],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.4085467,0.01848132,0.2700025,0.007858655,0.00151604,0.0001919373,0.001065919,0.0008428742,0.291494],"genre_scores_gemma":[0.9499453,0.002623606,0.02033626,0.0004763689,0.0005006253,0.00004699718,0.0002603789,0.0001006583,0.02570977],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.005218809,"threshold_uncertainty_score":0.01745862,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.008042243310463973,"score_gpt":0.237877926616436,"score_spread":0.229835683305972,"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."}}