{"id":"W2062613496","doi":"10.1007/bf02921863","title":"On a Step 2(k + 1) sub-Riemannian manifold","year":2004,"lang":"en","type":"article","venue":"Journal of Geometric Analysis","topic":"Geometric Analysis and Curvature Flows","field":"Mathematics","cited_by":18,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Toronto","funders":"","keywords":"Riemannian manifold; Geodesic; Exponential map (Riemannian geometry); Riemannian geometry; Pseudo-Riemannian manifold; Point (geometry); Manifold (fluid mechanics); Hermitian manifold; Mathematics; Riemannian submersion; Pure mathematics; Fundamental theorem of Riemannian geometry; Minimal volume; Solving the geodesic equations; Mathematical analysis; Ricci curvature; Scalar curvature; Geometry; Sectional 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":"codex-gemma-dda1882f352a","candidate_categories":["bibliometrics"],"consensus_categories":["bibliometrics"],"category_scores_codex":[0.001907587,0.0003158417,0.001350968,0.0119422,0.0001358635,0.0001377092,0.0005932418,0.000183739,0.0005636697],"category_scores_gemma":[0.002555299,0.0002305603,0.002022877,0.03199155,0.00003269724,0.0002617955,0.00005523041,0.0005619749,0.00008858502],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0002956461,"about_ca_system_score_gemma":0.0001046379,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00004874757,"about_ca_topic_score_gemma":0.00006016524,"domain_scores_codex":[0.9961808,0.00009498578,0.001352144,0.0002992308,0.001644139,0.0004287084],"domain_scores_gemma":[0.9961091,0.0007192045,0.001519547,0.0005796243,0.0007453205,0.0003271672],"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":[0.001391595,0.01751332,0.09095451,0.0005646479,0.167055,0.005099857,0.002195537,0.1246838,0.0006890334,0.3800527,0.1114819,0.09831815],"study_design_scores_gemma":[0.02540348,0.01069148,0.2430566,0.000785289,0.1780524,0.001252874,0.005798419,0.004292723,0.004736926,0.4791171,0.04071377,0.006098975],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.7205989,0.001207838,0.2750715,0.0006353412,0.0001798532,0.00009592472,0.000006712023,0.00002736458,0.002176516],"genre_scores_gemma":[0.9901431,0.0002321016,0.008409183,0.0002033414,0.0002455596,0.000001934321,0.000003689268,0.00002799907,0.0007331179],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.2695441,"threshold_uncertainty_score":0.9992566,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02116645657293518,"score_gpt":0.277057794828282,"score_spread":0.2558913382553468,"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."}}