Deformational rigidity of integrable metrics on the torus
Fuente:
arXiv
Guardado en:
| Autor principal: | |
|---|---|
| Formato: | Preprint |
| Publicado: |
2022
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866915102474633216 |
|---|---|
| author | Henheik, Joscha |
| author_facet | Henheik, Joscha |
| contents | It is conjectured that the only integrable metrics on the two-dimensional torus are Liouville metrics. In this paper, we study a deformative version of this conjecture: We consider integrable deformations of a non-flat Liouville metric in a conformal class and show that for a fairly large class of such deformations the deformed metric is again Liouville. Since our method of proof immediately carries over to higher dimensional tori, we obtain analogous statements in this more general case. In order to put our results in perspective, we review existing results about integrable metrics on the torus. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_02961 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Deformational rigidity of integrable metrics on the torus Henheik, Joscha Dynamical Systems Mathematical Physics Differential Geometry 37J35, 37J39, 53D25, 37C83, 37J40, 70H06 It is conjectured that the only integrable metrics on the two-dimensional torus are Liouville metrics. In this paper, we study a deformative version of this conjecture: We consider integrable deformations of a non-flat Liouville metric in a conformal class and show that for a fairly large class of such deformations the deformed metric is again Liouville. Since our method of proof immediately carries over to higher dimensional tori, we obtain analogous statements in this more general case. In order to put our results in perspective, we review existing results about integrable metrics on the torus. |
| title | Deformational rigidity of integrable metrics on the torus |
| topic | Dynamical Systems Mathematical Physics Differential Geometry 37J35, 37J39, 53D25, 37C83, 37J40, 70H06 |
| url | https://arxiv.org/abs/2210.02961 |