Wait, does the word “circle” here refer to a submanifold diffeomorphic to $S^1$ or to a bona fide Euclidean circle (set of points on a plane at equal distance from a center point)? Because the question is about the latter, but Vogt's paper mentions circles in a manifold, which can only make sense in the former sense. (Maybe there's an argument to reduce one to the other, however. I don't see one.)
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