| Autor: |
Kawamata, Masahiro, Shibuya, Kazuhiro |
| Rok vydání: |
2020 |
| Předmět: |
|
| Druh dokumentu: |
Working Paper |
| Popis: |
We discuss Monge-Amp\`ere equations from the view point of differential geometry. It is known that a Monge-Amp\`ere equation corresponds to a special exterior differential system on a 1-jet space. In this paper, we generalize Monge-Amp\`ere equations and prove that a $(k+1)$st order generalized Monge-Amp\`ere 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. |
| Databáze: |
arXiv |
| Externí odkaz: |
|
