On the Curvature of Regge Metrics

Evan S. Gawlik; Jack McKee

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arXiv · 2510.25027

On the Curvature of Regge Metrics

Evan S. Gawlik·Jack McKee

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Abstract

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.

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BibTeX RIS

Evan S. Gawlik, Jack McKee. 2025-10-28. On the Curvature of Regge Metrics. https://arxiv.org/abs/2510.25027

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