Abstract
In this paper, we will show that every sub-Riemannian manifold is the Gromov–Hausdorff limit of a sequence of Riemannian manifolds.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Agrachev, A.: Some open problems. In: Geometric Control Theory and Sub-Riemannian Geometry, Volume 5 of the series Springer INdAM Series, pp. 1–13, 2014
Agrachev, A., Barilari, D., Boscain, U.: Introduction to Riemannian and Sub-Riemannian Geometry, Preprint SISSA, 2013
Agrachev, A., Barilari, D., Boscain, U.: On the Hausdorff volume in sub-Riemannian geometry. Calc. Var. Partial Differentia. Equations, 43, 355–388 (2012)
Agrachev, A., Lee, P.: Generalized Ricci curvature bounds for three dimensional contact subriemannian manifolds. Math. Ann., 360, 209–253 (2014)
Agrachev, A., Lee, P.: Optimal transportation under nonholonomic constraints. Trans. Amer. Math. Soc., 361, 6019–6047 (2009)
Burago, D., Burago, Y., Ivanov, S.: A Course in Metric Geometry. Graduate Studies in Mathematics (Book 33), American Mathematical Society, Providence, RI, 2001
Donne, E. L.: Lipschitz and path isometric embeddings of metric spaces. Geometria. Dedicata, 166, 47–66 (2013)
Do Carmo, D. P.: Riemannian Geometry, Mathematics: Theory and Applications, Birkhauser, Boston, 1992
Acknowledgements
I wish to thank my supervisor of postgraduate Professor Fuquan Fang for introducing me in the study of the sub-Riemannian geometry.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Huang, Y.H. Every sub-Riemannian manifold is the Gromov–Hausdorff limit of a sequence Riemannian manifolds. Acta. Math. Sin.-English Ser. 33, 1565–1568 (2017). https://doi.org/10.1007/s10114-017-4543-x
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10114-017-4543-x