Abstract of "Quasi-contact S-R Metrics: normal form in $\RR^{2n}$, wave front and caustic in $\RR^{4}$".

This paper deals with sub-Riemannian metrics in the quasi-contact case. First, in any even dimension, we construct normal coordinates, a normal form and invariants, which are the analogs of normal coordinates, normal form and classical invariants in Riemannian geometry. Second, in dimension 4, and thanks to this "normal form", we study the local singularities of the exponential map.