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arXiv · 1511.05883

H\"ormander's condition for normal bundles on spaces of immersions

Martin Bauer·Philipp Harms
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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.

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Martin Bauer, Philipp Harms. 2015-11-18. H\"ormander's condition for normal bundles on spaces of immersions. https://doi.org/10.5281/zenodo.33558

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