Mathematics

The class of curves in the plane that L. Euler called elasticae in 1744 admit natural generalizations to arbitrary Riemannian manifolds M as the projections of solution curves of certain variational problems on the ortonormal frame bundle of M. For manifolds in which the frame bundle coincides with the isometry group, the elastic curves show remarkable connections with the movements of multi-dimensional mechanical tops. These, somewhat mysterious connections between tops, elastic curves and problems of optimal control constitute a major theme of the talk.