Zoll surface

In mathematics, particularly in differential geometry, a Zoll surface, named after Otto Zoll, 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 that are still Zoll surfaces.

In particular, most Zoll surfaces do not have constant curvature.

Zoll, a student of David Hilbert, discovered the first non-trivial examples.

This topology-related article is a stub.