2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/64476We compare Hofer's geometries on two spaces associated with a closed symplectic manifold M. The first space is the group of Hamiltonian diffeomorphisms. The second space L consists of all Lagrangian submanifolds of $M \times M$ which are exact Lagrangian isotopic to the diagonal. We show that in the case of a closed symplectic manifold with $π_2(M) = 0$, the canonical embedding of Ham(M) into L, f $\mapsto$ graph(f) is not an isometric embedding, although it preserves Hofer's length of smooth paths.Latex, 8 pagesSymplectic Geometry53d05text