On a generalization of Monge-Ampère equations and Monge-Ampère systems

2020/08/24 by M. Kawamata, Kawamata, Masahiro, Kazuhiro Shibuya +1
Mathematics · Physics and Astronomy · #58A15 #58A17 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.2008.10203

openalex publication_date 2020/08/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We discuss Monge-Ampère equations from the view point of differential geometry. It is known that a Monge-Ampère equation corresponds to a special exterior differential system on a 1-jet space. In this paper, we generalize Monge-Ampère equations and prove that a (k+1)st order generalized Monge-Ampère equation corresponds to a special exterior differential system on a k-jet space. Then its solution naturally corresponds to an integral manifold of the corresponding exterior differential system. Moreover, we verify that the Korteweg-de Vries (KdV) equation and the Cauchy-Riemann equations are examples of our equation.

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