学术报告（Sorin V. SABAU 12.26）
On the geometry of positively curved Zoll surfaces(具有正曲率的Zoll 曲⾯面的⼏几何 )
Zoll surfaces are classical examples of Riemannian surfaces all of whose geodesics are closed with same period. We will show that on the manifolds of geodesics of such a Riemannian metric there exist a natural induced Finsler metric of constant flag curvature K=1. Our research proves that the most natural geometrical objects on the manifold of geodesics of a Zoll metric are Finsler structures and not Riemannian ones. Moreover, our Finsler metrics of constant flag curvature K=1 are actually defined on the 2-dimensional sphere and depend on one arbitrary odd function of one variable, showing in this way the difference with the Riemannian case.