On Local Metric Characteristics of Level Sets of C1H-Mappings of Carnot Manifolds

Abstract

Considering the level surfaces of the mappings of class C1 which are defined on Carnot manifolds and take values in Carnot—Caratheodory spaces, we introduce some adequate local metric characteristic that bases on a correspondence with a neighborhood of the kernel of the sub-Riemannian differential. Moreover, for the mappings on Carnot groups we construct an adapted basis in the preimage which matches local sub-Riemannian structures on the complement of the kernel of the sub-Riemannian differential (including those meeting the level set) and on the arrival set.