Sard property for rank 2 polarizations in metabelian Lie groups

Abstract

We provide bounds on the dimension of the abnormal set for rank 2 polarizations on metabelian Lie groups, establishing the Sard property for the end-point map of such groups. We also obtain bounds for the dimension of the Goh-abnormal set for metabelian Lie groups where the codimension of the derived subgroup is at most 2, with no assumption on the rank of the polarization. We thus infer that these polarized groups, equipped with sub-Riemannian structures, satisfy the minimizing Sard property.