Journal of Symplectic Geometry

Volume 18 (2020)

Number 2

Volume of small balls and sub-Riemannian curvature in 3D contact manifolds

Pages: 355 – 384

DOI: https://dx.doi.org/10.4310/JSG.2020.v18.n2.a1

Authors

Davide Barilari (UFR Mathématiques, Université Paris Diderot, Paris, France)

Ivan Beschastnyi (Scuola Internazionale Superiore di Studi Avanzati (SISSA), Trieste, Italy)

Antonio Lerario (Scuola Internazionale Superiore di Studi Avanzati (SISSA), Trieste, Italy)

Abstract

We compute the asymptotic expansion of the volume of small sub-Riemannian balls in a contact $3$‑dimensional manifold, and we express the first meaningful geometric coefficients in terms of geometric invariants of the sub-Riemannian structure.

Received 8 May 2018

Accepted 30 April 2019

Published 8 June 2020