{"id":"W2001450985","doi":"10.4153/cmb-2011-108-1","title":"Chen Inequalities for Submanifolds of Real Space Forms with a Semi-Symmetric Non-Metric Connection","year":2011,"lang":"en","type":"article","venue":"Canadian Mathematical Bulletin","topic":"Geometric Analysis and Curvature Flows","field":"Mathematics","cited_by":28,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"European Social Fund","keywords":"Mathematics; Connection (principal bundle); Scalar curvature; Metric connection; Sectional curvature; Pure mathematics; Space form; Chen; Curvature; Mathematical analysis; Metric (unit); Space (punctuation); Fubini–Study metric; Complex space; Ricci curvature; Metric space; Injective metric space; Geometry; Intrinsic metric; Fundamental theorem of Riemannian geometry; Submanifold","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":"codex-gemma-dda1882f352a","candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.001013762,0.0002928694,0.000753527,0.001337191,0.0001167874,0.00004040962,0.0002949178,0.0002322998,0.00387269],"category_scores_gemma":[0.001920881,0.0002168998,0.0002331892,0.002074391,0.00009426449,0.00006140986,0.00002807688,0.000174128,0.0002404151],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001702989,"about_ca_system_score_gemma":0.0002006698,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00471023,"about_ca_topic_score_gemma":0.003796338,"domain_scores_codex":[0.9979951,0.00004263973,0.0006471005,0.0003308371,0.0003805499,0.0006037905],"domain_scores_gemma":[0.997417,0.0009472335,0.0003174141,0.0004884464,0.0003529145,0.0004769373],"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":[0.00008268486,0.0002849716,0.001057927,0.001220478,0.0003590494,0.00001784731,0.001929781,0.000002251823,0.00002063258,0.9810358,0.01335442,0.0006341803],"study_design_scores_gemma":[0.005131029,0.003139016,0.006098952,0.000869497,0.00234079,0.0001599504,0.0162526,0.002356229,0.004012246,0.9170271,0.04003525,0.002577414],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.6583564,0.0001537234,0.08832554,0.0007996598,0.00009516699,0.001868806,0.0001295238,0.0001174867,0.2501537],"genre_scores_gemma":[0.9761272,0.00001360896,0.01924441,0.00008472842,0.00005806991,0.0001292782,0.00001721303,0.00005893314,0.004266559],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.3177708,"threshold_uncertainty_score":0.9970379,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03879814671851396,"score_gpt":0.2455210288599062,"score_spread":0.2067228821413923,"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."}}