Vanishing geodesic distance on spaces of submanifolds and diffeomorphisms.
Variational calculus on Lie algebroids
It is shown that the Lagrange's equations for a Lagrangian system on a Lie algebroid are obtained as the equations for the critical points of the action functional defined on a Banach manifold of curves. The theory of Lagrangian reduction and the relation with the method of Lagrange multipliers are also studied.