Euler-like Vector Fields and Normal Forms

A vector field on a manifold is “Euler-like” with respect to a submanifold if its linear approximation is the Euler vector field on the normal bundle. We show that such a vector field canonically determines a tubular neighborhood embedding, and use this fact to obtain several normal form results in differential geometry. This talk is based in part on work with Francis Bischoff, Henrique Bursztyn, Hudson Lima, and Yiannis Loizides.