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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
REFERENCES
M. B. Karmanova, Izv.: Math. 78 (3), 475–499 (2014).
M. B. Karmanova, Dokl. Math. 98 (1), 360–363 (2018).
B. Franchi, R. Serapioni, and F. Serra Cassano, Math. Ann. 321, 479–531 (2001).
S. G. Basalaev, Vestn. Novosib. Gos. Univ. 13 (4), 16–36 (2013).
A. Kozhevnikov, Thèse de doctorat en Mathématiques (Universite Paris Sud, Paris, 2015).
B. Franchi and R. Serapioni, J. Geom. Anal. 26 (3), 1946–1994 (2016).
S. G. Basalaev and S. K. Vodopyanov, Eurasian Math. J. 4 (2), 10–48 (2013).
M. Karmanova and S. Vodopyanov, in Analysis and Mathematical Physics (Birkhäuser, Basel, 2009), pp. 233–335.
M. M. Postnikov, Lectures in Geometry, Semester V: Lie Groups and Lie Algebras (Nauka, Moscow, 1982).
S. Vodopyanov, “Geometry of Carnot–Carathéodory spaces and differentiability of mappings,” in The Interaction of Analysis and Geometry: Contemporary Mathematics (Am. Math. Soc., Providence, RI, 2007), pp. 247–301.
M. Karmanova and S. Vodopyanov, Acta Appl. Math. 128 (1), 67–111 (2013).
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated by I. Ruzanova
Rights and permissions
About this article
Cite this article
Karmanova, M.B. Local Metric Properties of Level Surfaces on Carnot–Carathéodory Spaces. Dokl. Math. 99, 75–78 (2019). https://doi.org/10.1134/S1064562419010241
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S1064562419010241