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arXiv · 1602.08745

Volume geodesic distortion and Ricci curvature for Hamiltonian dynamics

Andrei Agrachev·Davide Barilari·Elisa Paoli
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Abstract

We study the variation of a smooth volume form along extremals of a variational problem with nonholonomic constraints and an action-like Lagrangian. We introduce a new invariant describing the interaction of the volume with the dynamics and we study its basic properties. We then show how this invariant, together with curvature-like invariants of the dynamics, appear in the expansion of the volume at regular points of the exponential map. This generalizes the well-known expansion of the Riemannian volume in terms of Ricci curvature to a wide class of geometric structures, including all sub-Riemannian manifolds.

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BibTeXRIS

Andrei Agrachev, Davide Barilari, Elisa Paoli. 2016-02-28. Volume geodesic distortion and Ricci curvature for Hamiltonian dynamics. https://arxiv.org/abs/1602.08745

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