On the Berwald-Weyl Curvature
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866916318258659328 |
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| author | Shen, Zhongmin Sun, Liling |
| author_facet | Shen, Zhongmin Sun, Liling |
| contents | In this paper, we study the Berwald-Weyl curvature which is defined for a spray/Finsler metric with a volume form. We obtain some expressions for the Berwald-Weyl curvature. This quantity is a projective invariant with respect to a fixed volume form. We prove that for any spray of scalar curvature on a manifold of dimension $n\geq 3$, the Berwald-Weyl curvature vanishes with respect to any volume form. We also show that for any Finsler metric of constant Ricci curvature and constant S-curvature, the Berwald-Weyl curvature vanishes with respect to the Busemann-Hausdorff volume form. This study leads to a new notion of BWeyl-flat sprays/Finsler metrics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_07272 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the Berwald-Weyl Curvature Shen, Zhongmin Sun, Liling Differential Geometry In this paper, we study the Berwald-Weyl curvature which is defined for a spray/Finsler metric with a volume form. We obtain some expressions for the Berwald-Weyl curvature. This quantity is a projective invariant with respect to a fixed volume form. We prove that for any spray of scalar curvature on a manifold of dimension $n\geq 3$, the Berwald-Weyl curvature vanishes with respect to any volume form. We also show that for any Finsler metric of constant Ricci curvature and constant S-curvature, the Berwald-Weyl curvature vanishes with respect to the Busemann-Hausdorff volume form. This study leads to a new notion of BWeyl-flat sprays/Finsler metrics. |
| title | On the Berwald-Weyl Curvature |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2407.07272 |