Local metric properties of level surfaces on Carnot–Caratheodory spaces

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Abstract

For level sets of -mappings of Carnot manifolds to Carnot–Caratheodory spaces, we introduce an adequate local metric characteristic. Moreover, for mappings defined on Carnot groups, we construct a special adapted basis in the preimage such that it assigns a suitable local sub-Riemannian structure on a complement of a kernel of a sub-Riemannian differential to the initial sub-Riemannian structure in the image.

About the authors

M. B. Karmanova

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences

Author for correspondence.
Email: maryka@math.nsc.ru
Russian Federation, 4, Acad. Koptyug prospect, Novosibirsk, 630090

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