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

TL;DR

This paper derives the asymptotic expansion for the volume of small sub-Riemannian balls in 3D contact manifolds, linking geometric coefficients to invariants of the structure.

Contribution

It provides explicit formulas for the volume expansion in 3D contact manifolds, connecting geometric coefficients to sub-Riemannian invariants for the first time.

Findings

Explicit asymptotic volume expansion derived

Geometric coefficients expressed in terms of invariants

Enhanced understanding of sub-Riemannian geometry in 3D contact manifolds

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