Sub-Riemannian balls in CR Sasakian manifolds

TL;DR

This paper establishes global estimates for sub-Riemannian distances in CR Sasakian manifolds with non-negative Ricci curvature, showing that large sub-Riemannian balls are comparable to Riemannian balls, thus linking these geometric structures.

Contribution

It provides the first global estimates relating sub-Riemannian and Riemannian balls in CR Sasakian manifolds with non-negative Ricci curvature.

Findings

Large sub-Riemannian balls are comparable to Riemannian balls in this setting

Global estimates for sub-Riemannian distances are established

Results apply to CR Sasakian manifolds with non-negative Webster-Tanaka Ricci curvature

Abstract

We prove global estimates for the sub-Riemannian distance of CR Sasakian manifolds with non negative horizontal Webster-Tanaka Ricci curvature. In particular, in this setting, large sub-Riemannian balls are comparable to Riemannian balls.