On the Curvature of Regge Metrics
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866910007175413760 |
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| author | Gawlik, Evan S. McKee, Jack |
| author_facet | Gawlik, Evan S. McKee, Jack |
| contents | We use moving frame techniques to derive a notion of curvature for a class of piecewise-smooth Riemannian metrics called Regge metrics, showing that it is a measure that simultaneously satisfies the (weak) Cartan structure equations and the appropriate gauge transformation law. It turns out that this distributional curvature is equivalent to existing notions of densitized distributional curvature. We also investigate more closely the n = 2 case, where we prove the Gauss-Bonnet theorem for Regge metrics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_25027 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the Curvature of Regge Metrics Gawlik, Evan S. McKee, Jack Differential Geometry 53A70 We use moving frame techniques to derive a notion of curvature for a class of piecewise-smooth Riemannian metrics called Regge metrics, showing that it is a measure that simultaneously satisfies the (weak) Cartan structure equations and the appropriate gauge transformation law. It turns out that this distributional curvature is equivalent to existing notions of densitized distributional curvature. We also investigate more closely the n = 2 case, where we prove the Gauss-Bonnet theorem for Regge metrics. |
| title | On the Curvature of Regge Metrics |
| topic | Differential Geometry 53A70 |
| url | https://arxiv.org/abs/2510.25027 |