The symmetry group of a curve preserves a plane
The symmetry group of a curve preserves a plane
It is shown that the symmetries of a closed curve without self-intersections in euclidean or hyperbolic <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="n"> <mml:semantics> <mml:mi>n</mml:mi> <mml:annotation encoding="application/x-tex">n</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-space have an invariant plane in common. This allows a complete characterization of the symmetry group.