2018/08/01 by Goo Ishikawa, Ishikawa, Goo, Yumiko Kitagawa +5
Mathematics · Physics and Astronomy · #53A20 #53C17 #58A30 (Primary) 53A55 #70F25 (Secondary) #Advanced Differential Geometry Research #Cone (formal languages) #Differential Geometry (math.DG) #Distribution (mathematics) #Dual cone and polar cone #Duality (order theory) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry #Geometry and complex manifolds #Lagrangian #Manifold (fluid mechanics) #Mathematical analysis #Mathematics #Physics #Pure mathematics #math.DG #msc:53A20 #msc:53A55 #msc:53C17 #msc:58A30 #msc:70F25
paper · pdf · doi:10.48550/arxiv.1808.00149
13 pages
arxiv created 2018/08/01 · openalex publication_date 2018/08/01 · arxiv updated 2018/08/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
As was shown by a part of the authors, for a given (2, 3, 5)-distribution D on a 5-dimensional manifold Y, there is, locally, a Lagrangian cone structure C on another 5-dimensional manifold X which consists of abnormal or singular paths of (Y, D). We give a characterization of the class of Lagrangian cone structures corresponding to (2, 3, 5)-distributions. Thus we complete the duality between (2, 3, 5)-distributions and Lagrangian cone structures via pseudo-product structures of type G2. A local example of non-flat perturbations of the global model of flat Lagrangian cone structure which corresponds to (2,3,5)-distributions is given.