Minimal Timelike Surfaces in the Lorentz-Minkowski 3-space and Their Canonical Parameters
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2023
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866910348126191616 |
|---|---|
| author | Kassabov, Ognian Milousheva, Velichka |
| author_facet | Kassabov, Ognian Milousheva, Velichka |
| contents | We study minimal timelike surfaces in $\mathbb R^3_1$ using a special Weierstrass-type formula in terms of holomorphic functions defined in the algebra of the double (split-complex) numbers. We present a method of obtaining an equation of a minimal timelike surface in terms of canonical parameters, which play a role similar to the role of the natural parameters of curves in $\mathbb R^3$. Having one holomorphic function that generates a minimal timelike surface, we find all holomorphic functions that generate the same surface. In this way we give a correspondence between a minimal timelike surface and a class of holomorphic functions. As an application, we prove that the Enneper surfaces are the only minimal timelike surfaces in $\mathbb R^3_1$ with polynomial parametrization of degree 3 in isothermal parameters. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_10129 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Minimal Timelike Surfaces in the Lorentz-Minkowski 3-space and Their Canonical Parameters Kassabov, Ognian Milousheva, Velichka Differential Geometry 53A10, 53B30, 53C50 We study minimal timelike surfaces in $\mathbb R^3_1$ using a special Weierstrass-type formula in terms of holomorphic functions defined in the algebra of the double (split-complex) numbers. We present a method of obtaining an equation of a minimal timelike surface in terms of canonical parameters, which play a role similar to the role of the natural parameters of curves in $\mathbb R^3$. Having one holomorphic function that generates a minimal timelike surface, we find all holomorphic functions that generate the same surface. In this way we give a correspondence between a minimal timelike surface and a class of holomorphic functions. As an application, we prove that the Enneper surfaces are the only minimal timelike surfaces in $\mathbb R^3_1$ with polynomial parametrization of degree 3 in isothermal parameters. |
| title | Minimal Timelike Surfaces in the Lorentz-Minkowski 3-space and Their Canonical Parameters |
| topic | Differential Geometry 53A10, 53B30, 53C50 |
| url | https://arxiv.org/abs/2310.10129 |