On Local Metric Characteristics of Level Sets of CH1-Mappings of Carnot Manifolds

Abstract

Considering the level surfaces of the mappings of class C_H¹ which are defined on Carnot manifolds and take values in Carnot—Carathéodory 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.