{"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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0002980244,0.001242464,0.0008269886,0.002414174,0.001646759,0.00196364,0.001400934,0.002217292,0.00623358],"category_scores_gemma":[0.0009137461,0.0004937478,0.0008286044,0.0007592042,0.002035223,0.002168298,0.002165938,0.001388414,0.001586058],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001195328,"about_ca_system_score_gemma":0.0005488707,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.002587662,"about_ca_topic_score_gemma":0.002840915,"domain_scores_codex":[0.9996909,0.00005816626,0.00001523668,0.00006306064,0.00009448981,0.00007818978],"domain_scores_gemma":[0.9994443,0.0000796574,0.0001372867,0.00005862494,0.00009696612,0.0001831966],"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":[0.0002106044,0.00011044,0.001976296,0.0000779755,0.0000415164,0.001381533,0.0007052495,0.01231307,0.01402045,0.9573205,0.00313374,0.008708525],"study_design_scores_gemma":[0.00005929006,0.000327122,0.006212112,0.0000351013,0.00004118347,0.001114147,0.0005982875,0.141229,0.003825642,0.8371206,0.009354562,0.00008291425],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8819306,0.0003446737,0.07144979,0.001345957,0.0003015645,0.00009135082,0.0003285694,0.0002609741,0.04394642],"genre_scores_gemma":[0.9376471,0.0002925792,0.01596446,0.0002164175,0.0001506089,0.00004240841,0.00032319,0.0001177467,0.04524545],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.00623358,"threshold_uncertainty_score":0.0208534,"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."}}