Compact 3-manifolds with a flat Carnot-Carathéodory metric

Jacek Świątkowski

Colloquium Mathematicae (1992)

  • Volume: 63, Issue: 1, page 89-105
  • ISSN: 0010-1354

How to cite


Świątkowski, Jacek. "Compact 3-manifolds with a flat Carnot-Carathéodory metric." Colloquium Mathematicae 63.1 (1992): 89-105. <>.

author = {Świątkowski, Jacek},
journal = {Colloquium Mathematicae},
keywords = {Carnot-Carathéodory metric; Heisenberg group; holonomy group},
language = {eng},
number = {1},
pages = {89-105},
title = {Compact 3-manifolds with a flat Carnot-Carathéodory metric},
url = {},
volume = {63},
year = {1992},

AU - Świątkowski, Jacek
TI - Compact 3-manifolds with a flat Carnot-Carathéodory metric
JO - Colloquium Mathematicae
PY - 1992
VL - 63
IS - 1
SP - 89
EP - 105
LA - eng
KW - Carnot-Carathéodory metric; Heisenberg group; holonomy group
UR -
ER -


  1. [A] L. Auslander, Bieberbach's theorems on space groups and discrete uniform subgroups of Lie groups, Ann. of Math. 71 (1960), 579-590. Zbl0099.25602
  2. [G] M. Gromov, Structures métriques pour les variétés riemanniennes, notes de cours rédigées par J. Lafontaine et P. Pansu, Textes Math. 1, CEDIC, Paris 1981. 
  3. [H] U. Hamenstädt, Zur Theorie von Carnot-Carathéodory Metriken und ihren Anwendungen, Dissertation, Univ. Bonn, 1986, Bonner Math. Schriften 180, 1987. Zbl0648.53026
  4. [M] J. Mitchell, On Carnot-Carathéodory metrics, J. Differential Geom. 21 (1985), 35-45. Zbl0554.53023
  5. [P] P. Pansu, Métriques de Carnot-Carathéodory et quasiisométries des espaces symétriques de rang un, Ann. of Math. 129 (1989), 1-60. Zbl0678.53042
  6. [R] M. S. Raghunathan, Discrete Subgroups of Lie Groups, Springer, Berlin 1972. Zbl0254.22005
  7. [V-G] A. M. Vershik and V. Ya. Gershkovich, Nonholonomic problems and the geometry of distributions (in Russian), appendix to the Russian edition of: P. Griffiths, Exterior Differential Systems and Variational Calculus, Nauka, Moscow 1986. 
  8. [W] J. Wolf, Spaces of Constant Curvature, McGraw-Hill, 1967. Zbl0162.53304

NotesEmbed ?


You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.


Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.