The simple length spectrum of a Riemannian manifold is the set of lengths of its simple closed geodesics. We prove that in any Riemannian 2-sphere whose simple length spectrum consists of only one element L, any geodesic is simple closed with length L. We also show that, if the simple length spectrum of a Riemannian 2-sphere contains at most two elements, for at least one such element L every point of the 2-sphere lies on a simple closed geodesic of length L. 查看全文>>