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The simple length spectrum of a Riemannian manifold is the set of lengths of its simple closed geodesics. We prove a theorem claimed by Lusternik: in any Riemannian 2‐sphere whose simple length spectrum consists of only one element   ℓ  , any geodesic is simple closed with length   ℓ  .

A characterization of Zoll Riemannian metrics on the 2‐sphere