On the spectral characterization of Besse and Zoll Reeb flows

A closed contact manifold is called Besse when all its Reeb orbits are closed, and Zoll they have the same minimal period. In this paper, we provide a characterization of forms for convex spheres Riemannian unit tangent bundles in terms $S^1$-equivariant spectral invariants. Furthermore, restricted type hypersurfaces symplectic Euclidean spaces, give sufficient condition property via Ekeland-Hofer capacities.