Normal forms for the sub-Riemannian exponential map of ${\mathbb{G}}_{\alpha }$, $\mathrm{SU}(2)$, and $\mathrm{SL}(2)$

Samuël Borza

The goal of this paper is to use singularity theory to find normal forms near the critical points of the sub-Riemannian exponential map. Three cases are studied: the $\alpha$-Grushin pl…