Universität Augsburg
Institut für Mathematik

Please ask Prof. Urs Frauenfelder for­ login details.

Zoll Metrics, i.e. Riemannian metrics all of whose geodesics are closed of coinciding length, are well a studied problem in geometry with at the same time many open questions. Especially exact characterizations in terms of other geometric properties are not numerous. One idea is to use the Morse theory of energy/length functional on the loop space for this problem. It is easy to see that for Zoll metrics the critical manifolds are diffeomorphic to the unit tangent bundle of the underlying space. The counter direction is much less obvious. I will discuss how this can be achieved for the $2$-sphere by elementary arguments and give an idea how it can be generalized to higher dimensions. This is work in cooperation with Marco Mazzucchelli (ENS Lyon).