2003/06/30 by Pawel Nurowski, Pawe Nurowski, George Sparling +1
Mathematics · #Advanced Algebra and Geometry #Algebraic and Geometric Analysis #Cauchy distribution #Cauchy–Riemann equations #Conformal map #Differential equation #Discrete mathematics #Equivalence (formal languages) #Equivalence class (music) #Holomorphic and Operator Theory #Mathematical analysis #Mathematical physics #Mathematics #Modulo #Ode #Ordinary differential equation #Physics #Pure mathematics #Riemann surface #math.DG
paper · pdf · doi:10.1088/0264-9381/20/23/004
arxiv created 2003/09/24 · openalex publication_date 2003/10/20 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The equivalence problem for second-order ordinary differential equations (ODEs) given modulo point transformations is solved in full analogy with the equivalence problem of nondegenerate three-dimensional Cauchy–Riemann structures. This approach enables an analogue of the Fefferman metrics to be defined. The conformal class of these (split signature) metrics is well defined by each point equivalence class of second-order ODEs. Its conformal curvature is interpreted in terms of the basic point invariants of the corresponding class of ODEs.