2025/05/28 by Tomasz Sobczak, Sobczak, Tomasz, Tymon Frelik +1
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Differential Geometry (math.DG) #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #Geometric Analysis and Curvature Flows #Statistical Mechanics and Entropy
paper · pdf · doi:10.48550/arxiv.2505.22294
openalex publication_date 2025/05/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Our study of Goursat distributions originates new types of k-contact distributions and Lie systems with applications. In particular, families of generators for Goursat distributions on ℝ4, ℝ5 and ℝ6 give rise to Lie systems and we characterise Goursat structures that are k-contact distributions. Our results are used to study the zero-trailer and other systems via Lie systems and k-contact manifolds. New ideas for the development of superposition rules via geometric structures and the characterisation of k-contact distributions are given and applied. Some relations of k-contact geometry with parabolic Cartan geometries are inspected.