On caustics of submanifolds and canal hypersurfaces in Euclidean space

We investigate a relationship between the caustics of a submanifold of general dimension and of a canal hypersurface of the submanifold in Euclidean space. As a consequence, these caustics are the same. Moreover, induced Lagrangian immersion germs are Lagrangian equivalent under a suitable condition. In order to show the results, we use the theory of Lagrangian singularity and of Legendrian singularity.