Detlef Gromoll - Metric foliations and nonnegative curvature

Metric foliations of a riemannian space have leaves any two of which are locally everywhere equidistant, such as level sets of distance functions or orbits under isometric group actions. Aside from the intrinsic appeal of understanding such configurations both from a global and local point of view, they are playing an increasingly important role in other areas of geometry. They arise prominently in connection with rigidity aspects in the structure theory of nonnegatively curved manifolds, as well as in the construction of various types of examples by warping methods. We will discuss key ideas and developments in this direction, including recent progress in and the current state of classifying metric foliations in round spheres and euclidean spaces.