A local version of the Myers-Steenrod Theorem

Abstract

We prove the Myers-Steenrod theorem for local topological groups of isometries acting on pointed ${\mathcal{C}}^{k,\alpha }$-Riemannian manifolds, with $k+\alpha >0$. As an application, we infer a new regularity result for a certain class of locally homogeneous Riemannian metrics.

11 pages. Some minor modifications. Accepted for publication in Bull. Lond. Math. Soc