The question of existence of c10sed geodesics on a Riemannian manifold and the properties of the corresponding periodic orbits in the geodesic flow has been the

In 1854, B Riemann introduced the notion of curvature for spaces with a family of inner products. There was no significant progress in the general case until 19

Singular spaces with upper curvature bounds and, in particular, spaces of nonpositive curvature, have been of interest in many fields, including geometric (and