Hörmander's condition for normal bundles on spaces of immersions

Abstract

Several representations of geometric shapes involve quotients of mapping spaces. The projection onto the quotient space defines two sub-bundles of the tangent bundle, called the horizontal and vertical bundle. We investigate in these notes the sub-Riemannian geometries of these bundles. In particular, we show for a selection of bundles which naturally occur in applications that they are either bracket generating or integrable.

arXiv comment4 pages. (2015). Proceedings of Math On The Rocks Shape Analysis Workshop in Grundsund. Zenodo