Horizontal curvatures of surfaces in 3D contact sub-Riemannian Lie groups
Fuente:
arXiv
Guardado en:
| Autores principales: | , , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2026
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866914379933417472 |
|---|---|
| author | Bubani, Elia Pinamonti, Andrea Platis, Ioannis D. Tsolis, Dimitrios |
| author_facet | Bubani, Elia Pinamonti, Andrea Platis, Ioannis D. Tsolis, Dimitrios |
| contents | In this paper we study horizontal curvatures for surfaces embedded in three-dimensional contact sub-Riemannian Lie groups. Using a Riemannian approximation scheme, we derive explicit formulas for horizontal Gauss curvature, horizontal mean curvature, and symplectic distortion for surfaces embedded in three dimensional Lie groups with a sub-Riemannian structure obtained by a contact form. We focus on two primary examples: the Heisenberg group and the affine-additive group. We classify surfaces of revolution within these groups that exhibit constant horizontal curvatures, often expressing their profiles through elementary or elliptic integrals. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_08330 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Horizontal curvatures of surfaces in 3D contact sub-Riemannian Lie groups Bubani, Elia Pinamonti, Andrea Platis, Ioannis D. Tsolis, Dimitrios Differential Geometry 53C17, 53D10 In this paper we study horizontal curvatures for surfaces embedded in three-dimensional contact sub-Riemannian Lie groups. Using a Riemannian approximation scheme, we derive explicit formulas for horizontal Gauss curvature, horizontal mean curvature, and symplectic distortion for surfaces embedded in three dimensional Lie groups with a sub-Riemannian structure obtained by a contact form. We focus on two primary examples: the Heisenberg group and the affine-additive group. We classify surfaces of revolution within these groups that exhibit constant horizontal curvatures, often expressing their profiles through elementary or elliptic integrals. |
| title | Horizontal curvatures of surfaces in 3D contact sub-Riemannian Lie groups |
| topic | Differential Geometry 53C17, 53D10 |
| url | https://arxiv.org/abs/2603.08330 |