Asymmetric $\lambda$-deformed cosets

We study the integrable asymmetric $\lambda$-deformations of the $SO(n+1)/SO(n)$ coset models, following the prescription proposed in \cite{AsyLambda}. We construct all corresponding deformed geometries in an inductive way. Remarkably we find a $Z_2$ transformation which maps the asymmetric $\lambda$--deformed models to the symmetric $\lambda$--deformed models.