2012/10/18 by Takahiro Noda, Noda, Takahiro
Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Advanced Differential Geometry Research #Algebra over a field #Applied mathematics #Combinatorics #Decomposition #Differential Geometry (math.DG) #FOS: Mathematics #Mathematics #Nonlinear Waves and Solitons #Order (exchange) #Overdetermined system #Pure mathematics #Rank (graph theory) #Rank condition #Type (biology) #math.DG
paper · pdf · doi:10.48550/arxiv.1210.5112
arxiv created 2012/10/18 · openalex publication_date 2012/10/18 · arxiv updated 2012/10/19 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/06
The purpose of this present paper is to investigate the geometric structure of regular overdetermined systems of second order with two independent and one dependent variables from the point of view of rank 2 prolongations. Utilizing this notion of prolongations, we characterize the type of these overdetermined systems. We also give a systematic method for constructing the geometric singular solutions by analyzing of a decomposition of this prolongation. As an applications, we determine the geometric singular solutions of Cartan's overdetermined systems.