B01 Curvature and Symmetry

The question of how far geometric properties of a manifold determine its global topology is a
classical problem in global differential geometry. In a first subproject we study the topology of
positively curved manifolds with torus symmetry. We think that the methods used in this subproject can also be used to attack the Salamon conjecture for positive quaternionic Kähler manifolds. In a third subproject we study fundamental groups of non-negatively curved manifolds. Two other subprojects are concerned with the classification of manifolds all of whose geodesics are closed and the existence of closed geodesics on Riemannian orbifolds.