{"id":"W2077688369","doi":"10.4153/cjm-2010-013-4","title":"A Second Order Smooth Variational Principle on Riemannian Manifolds","year":2009,"lang":"en","type":"article","venue":"Canadian Journal of Mathematics","topic":"Geometric Analysis and Curvature Flows","field":"Mathematics","cited_by":3,"is_retracted":false,"has_abstract":true,"ca_institutions":"Thompson Rivers University","funders":"","keywords":"Mathematics; Sectional curvature; Order (exchange); Bounded function; Variational principle; Curvature of Riemannian manifolds; Riemannian geometry; Ricci-flat manifold; Regular polygon; Pure mathematics; Mathematical analysis; Curvature; Riemannian manifold; Scalar curvature; Geometry","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":[0.001872275,0.0008612884,0.0009181075,0.001091867,0.0008441242,0.0017688,0.0009013673,0.001401213,0.002155858],"category_scores_gemma":[0.001874126,0.0005286862,0.001188264,0.0003130996,0.002846339,0.00212858,0.003837169,0.001975268,0.0003134694],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001323186,"about_ca_system_score_gemma":0.001027943,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001065903,"about_ca_topic_score_gemma":0.0008882199,"domain_scores_codex":[0.9994034,0.0001518866,0.00001926667,0.0001057765,0.000227371,0.00009234853],"domain_scores_gemma":[0.9991761,0.0002451524,0.00009105325,0.00007522191,0.0001904882,0.0002220639],"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":[0.0000143876,0.0000142831,0.0002595442,0.00003427648,0.00001676919,0.0001096972,0.0001164249,0.01124488,0.00572206,0.9800362,0.0004733381,0.001958256],"study_design_scores_gemma":[0.00002624455,0.0001520936,0.001045841,0.0000277116,0.00001653991,0.0003266151,0.00008853971,0.2565909,0.002291344,0.7340342,0.005365429,0.00003456552],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.2514816,0.0007644835,0.7043032,0.002425317,0.0002293971,0.00008991333,0.0001659453,0.0001905427,0.04034964],"genre_scores_gemma":[0.9294911,0.0003802037,0.04616034,0.0003702201,0.0002277174,0.0001010341,0.0001375462,0.0001318634,0.02300007],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.002155858,"threshold_uncertainty_score":0.009901643,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02656300601240481,"score_gpt":0.2698499709218516,"score_spread":0.2432869649094468,"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."}}