| Autor: |
Akbar Tayebi, Wei Sin Koh |
| Jazyk: |
angličtina |
| Rok vydání: |
2024 |
| Předmět: |
|
| Zdroj: |
Mathematics, Vol 12, Iss 13, p 2141 (2024) |
| Druh dokumentu: |
article |
| ISSN: |
2227-7390 |
| DOI: |
10.3390/math12132141 |
| Popis: |
Let (M,F) be a Finsler surface with the isotropic main scalar I=I(x). The well-known Berwald’s theorem states that F is a Berwald metric if and only if it has a constant main scalar I=constant. This ensures a kind of equality of two non-Riemannian quantities for Finsler surfaces. In this paper, we consider a positively curved Finsler surface and show that H=0 if and only if I=0. This provides an extension of Berwald’s theorem. It follows that F has an isotropic scalar flag curvature if and only if it is Riemannian. Our results yield an infrastructural development of some equalities for two-dimensional Finsler manifolds. |
| Databáze: |
Directory of Open Access Journals |
| Externí odkaz: |
|
