Abstract
The Popp measure of a sub-Riemannian ball is calculated for a left-invariant sub-Riemannian structure on the Heisenberg group.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
A. Bellaiche, “The tangent space in sub-Riemannian geometry,” Prog. Math., 144, 1–78 (1996).
R. Montgomery, A Tour of Subriemannian Geometries, Their Geodesies and Applications, AMS, Providence (2002).
E. F. Sachkova, “Solution of control problems for nilpotent systems,” Differ. Uravn., 44, No. 12, 1704–1707 (2008).
A. M. Vershik and V. H. Hershkowitz, “Nonholonomic dynamical systems and geometry of the distributions,” Results of Science and Technology. Current Problems in Mathematics. The Fundamental Direction. Dynamical Systems, 7, 8 (1986).
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated from Sovremennaya Matematika. Fundamental’nye Napravleniya (Contemporary Mathematics. Fundamental Directions), Vol. 42, Proceedings of the International Conference on Mathematical Control Theory and Mechanics (Suzdal, Russia, 3–7 July, 2009), Part 1, 2011.
Rights and permissions
About this article
Cite this article
Sachkova, E.F. Sub-Riemannian Balls on the Heisenberg Groups: An Invariant Volume. J Math Sci 199, 583–587 (2014). https://doi.org/10.1007/s10958-014-1885-0
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10958-014-1885-0