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Zoll surface
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<p>In mathematics, particularly in <a href="/facts/Differential_geometry/c04XmyLu">differential geometry</a>, a Zoll surface, named after Otto Zoll, is a <a href="/facts/Surface_(topology)/jK1b1KIG">surface</a> <a href="/facts/Homeomorphic/jMfWg3Mn">homeomorphic</a> to the <a href="/facts/2-sphere/jywYLNM2">2-sphere</a>, equipped with a <a href="/facts/Riemannian_metric/5KYnmEgF">Riemannian metric</a> all of whose <a href="/facts/Geodesic/fbWR6l80">geodesics</a> are <a href="/facts/Closed_geodesic/DlBzcCgT">closed</a> and of equal length. While the usual unit-sphere metric on <i>S</i>2 obviously has this property, it also has an infinite-dimensional family of geometrically distinct deformations that are still Zoll surfaces. In particular, most Zoll surfaces do not have constant <a href="/facts/Curvature_of_Riemannian_manifolds/1jYxPnzn">curvature</a>. </p><p>Zoll, a student of <a href="/facts/David_Hilbert/1vhlHn4b">David Hilbert</a>, discovered the first non-trivial examples. </p>