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arXiv · 1409.8378

Sub-Riemannian structures on groups of diffeomorphisms

Sylvain Arguillere·Emmanuel Trélat
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Abstract

In this paper, we define and study strong right-invariant sub-Riemannian structures on the group of diffeomorphisms of a manifold with bounded geometry. We derive the Hamiltonian geodesic equations for such structures, and we provide examples of normal and of abnormal geodesics in that infinite-dimensional context. The momentum formulation gives a sub-Riemannian version of the Euler-Arnol'd equation. Finally, we establish some approximate and exact reachability properties for diffeomorphisms, and we give some consequences for Moser theorems.

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Sylvain Arguillere, Emmanuel Trélat. 2015-01-22. Sub-Riemannian structures on groups of diffeomorphisms. https://doi.org/10.1017/s1474748015000249

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