On p-biharmonic curves
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_ | 1866911845339627520 |
|---|---|
| author | Branding, Volker |
| author_facet | Branding, Volker |
| contents | In this article we study $p$-biharmonic curves as a natural generalization of biharmonic curves. In contrast to biharmonic curves $p$-biharmonic curves do not need to have constant geodesic curvature if $p=\frac{1}{2}$ in which case their equation reduces to the one of $\frac{1}{2}$-elastic curves. We will classify $\frac{1}{2}$-biharmonic curves on closed surfaces and three-dimensional space forms making use of the results obtained for $\frac{1}{2}$-elastic curves from the literature. By making a connection to magnetic geodesic we are able to prove the existence of $\frac{1}{2}$-biharmonic curves on closed surfaces. In addition, we will discuss the stability of $p$-biharmonic curves with respect to normal variations. Our analysis highlights some interesting relations between $p$-biharmonic and $p$-elastic curves. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2206_15249 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | On p-biharmonic curves Branding, Volker Differential Geometry Dynamical Systems In this article we study $p$-biharmonic curves as a natural generalization of biharmonic curves. In contrast to biharmonic curves $p$-biharmonic curves do not need to have constant geodesic curvature if $p=\frac{1}{2}$ in which case their equation reduces to the one of $\frac{1}{2}$-elastic curves. We will classify $\frac{1}{2}$-biharmonic curves on closed surfaces and three-dimensional space forms making use of the results obtained for $\frac{1}{2}$-elastic curves from the literature. By making a connection to magnetic geodesic we are able to prove the existence of $\frac{1}{2}$-biharmonic curves on closed surfaces. In addition, we will discuss the stability of $p$-biharmonic curves with respect to normal variations. Our analysis highlights some interesting relations between $p$-biharmonic and $p$-elastic curves. |
| title | On p-biharmonic curves |
| topic | Differential Geometry Dynamical Systems |
| url | https://arxiv.org/abs/2206.15249 |