Sunada local isometry lemma
= Sunada local isometry lemma
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= Sunada's local isometry lemma
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On a compact smooth manifold without boundary of dimension at least two, a <residual set> of smooth <Riemannian metrics> consists of <nowhere locally homogeneous metrics>. Thus such metrics are dense in the smooth topology by the <Baire category theorem>. In dimension one, arclength coordinates always provide nontrivial <local isometries>.