Locally homogeneous $C^0$-Riemannian manifolds

TL;DR

This paper proves that any locally homogeneous continuous Riemannian manifold must actually be smooth, establishing a regularity result that bridges the gap between local homogeneity and differentiability.

Contribution

The paper demonstrates that local homogeneity in continuous Riemannian manifolds implies smoothness, a significant regularity result in differential geometry.

Findings

Locally homogeneous $C^0$-Riemannian manifolds are smooth.

Regularity of such manifolds is guaranteed by local homogeneity.

Bridges the gap between continuous and smooth structures in Riemannian geometry.

Abstract

We show that locally homogeneous $\mathcal{C}^0$-Riemannian manifolds are smooth.