Zoll Surface
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High Quality Content by WIKIPEDIA articles! A Zoll surface is a surface homeomorphic to the 2-sphere, equipped with a Riemannian metric all of whose geodesics are closed and of equal length. While the usual unit-sphere metric on S2 obviously has this property, it also has an infinite-dimensional family of geometrically distinct deformations which are still Zoll. In particular, most Zoll surfaces do not have constant curvature. Zoll surfaces are named after David Hilbert's student Otto Zoll, who discovered the first non-trivial examples.

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High Quality Content by WIKIPEDIA articles! A Zoll surface is a surface homeomorphic to the 2-sphere, equipped with a Riemannian metric all of whose geodesics are closed and of equal length. While the usual unit-sphere metric on S2 obviously has this property, it also has an infinite-dimensional family of geometrically distinct deformations which are still Zoll. In particular, most Zoll surfaces do not have constant curvature. Zoll surfaces are named after David Hilbert's student Otto Zoll, who discovered the first non-trivial examples.