Hyperbolic Monge-Ampère systems with $S_1=0$
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866908572565110784 |
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| author | Hu, Yuhao |
| author_facet | Hu, Yuhao |
| contents | For hyperbolic Monge-Ampère systems, a well-known solution of the equivalence problem yields two invariant tensors, ${S}_1$ and ${S}_2$, defined on the underlying $5$-manifold, where ${S}_2=0$ characterizes systems that are Euler-Lagrange. In this article, we consider the `opposite' case, ${S}_1 = 0$, and show that the local generality of such systems is `$2$ arbitrary functions of $3$ variables'. In addition, we classify all $S_1=0$ systems with cohomogeneity at most one, which turn out to be linear up to contact transformations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_21998 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Hyperbolic Monge-Ampère systems with $S_1=0$ Hu, Yuhao Differential Geometry Analysis of PDEs 35L10, 58A15, 53C10 For hyperbolic Monge-Ampère systems, a well-known solution of the equivalence problem yields two invariant tensors, ${S}_1$ and ${S}_2$, defined on the underlying $5$-manifold, where ${S}_2=0$ characterizes systems that are Euler-Lagrange. In this article, we consider the `opposite' case, ${S}_1 = 0$, and show that the local generality of such systems is `$2$ arbitrary functions of $3$ variables'. In addition, we classify all $S_1=0$ systems with cohomogeneity at most one, which turn out to be linear up to contact transformations. |
| title | Hyperbolic Monge-Ampère systems with $S_1=0$ |
| topic | Differential Geometry Analysis of PDEs 35L10, 58A15, 53C10 |
| url | https://arxiv.org/abs/2505.21998 |