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.

中文翻译：

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Myers–Steenrod定理的本地版本

我们证明了作用于尖点的局部等距拓扑群的Myers–Steenrod定理 ${\mathcal{C}}^{ķ，\alpha }$‐黎曼流形，具有 $ķ+\alpha >0$。作为应用程序，我们为一类局部齐次的黎曼度量推论出新的正则结果。