On Riemannian polyhedra with non-obtuse dihedral angles in 3-manifolds with positive scalar curvature
Fuente:
arXiv
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2022
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866913449135570944 |
|---|---|
| author | Yu, Li |
| author_facet | Yu, Li |
| contents | We determine the combinatorial types of all the 3-dimensional simple convex polytopes in R^3 that can be realized as mean curvature convex (or totally geodesic) Riemannian polyhedra with non-obtuse dihedral angles in Riemannian 3-manifolds with positive scalar curvature. This result can be considered as an analogue of Andreev's theorem on 3-dimensional hyperbolic polyhedra with non-obtuse dihedral angles. In addition, we construct many examples of such kind of simple convex polytopes in higher dimensions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2201_06059 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | On Riemannian polyhedra with non-obtuse dihedral angles in 3-manifolds with positive scalar curvature Yu, Li Differential Geometry Geometric Topology 51M20, 51F15, 52B10, 53C23, 57M50, 57S12 We determine the combinatorial types of all the 3-dimensional simple convex polytopes in R^3 that can be realized as mean curvature convex (or totally geodesic) Riemannian polyhedra with non-obtuse dihedral angles in Riemannian 3-manifolds with positive scalar curvature. This result can be considered as an analogue of Andreev's theorem on 3-dimensional hyperbolic polyhedra with non-obtuse dihedral angles. In addition, we construct many examples of such kind of simple convex polytopes in higher dimensions. |
| title | On Riemannian polyhedra with non-obtuse dihedral angles in 3-manifolds with positive scalar curvature |
| topic | Differential Geometry Geometric Topology 51M20, 51F15, 52B10, 53C23, 57M50, 57S12 |
| url | https://arxiv.org/abs/2201.06059 |