蒙日-安培方程及蒙日-安培系统的推广

Pub Date : 2022-01-01 DOI:10.3836/tjm/1502179374
M. Kawamata, K. Shibuya
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引用次数: 1

摘要

本文从微分几何的角度讨论了蒙日-安培方程。已知monge - ampantere方程对应于一个单射流空间上的特殊外微分系统。本文推广了monge - amp方程,证明了k-射流空间上的(k+ 1)st阶广义monge - ampante方程对应于一个特殊的外微分系统。那么它的解自然对应于相应外部微分系统的积分流形。此外,我们验证了Korteweg-de Vries (KdV)方程和Cauchy-Riemann方程是我们的方程的例子。2010年数学学科分类。主要58 a15;二级第a17 58。
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On a Generalization of Monge–Ampère Equations and Monge–Ampère Systems
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. 2010 Mathematics Subject Classification. Primary 58A15; Secondary 58A17.
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