Local Metric Properties of Level Surfaces on Carnot–Carathéodory Spaces

Abstract

An adequate local metric characteristic is introduced for level sets of \(C_{H}^{1}\)-mappings of Carnot manifolds to Carnot–Carathéodory spaces. Moreover, for mappings defined on Carnot groups, a special adapted basis in the preimage is constructed that assigns a suitable local sub-Riemannian structure on the complement of the kernel of a sub-Riemannian differential to the initial sub-Riemannian structure in the image.