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International Mathematics Research Notices (2008) Vol. 2008 : article ID rnn066, 35 pages, doi:10.1093/imrn/rnn066 published on June 27, 2008
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© The Author 2008. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oxfordjournals.org

On the Deformation Space of Clifford–Klein Forms of Heisenberg Groups

Ali Baklouti1, Imed Kédim2 and Taro Yoshino3

1 Department of Mathematics, Faculty of Sciences of Sfax, Route de Soukra, 3038, Sfax, Tunisia
1 Department of Mathematics, Faculty of Sciences of Bizerte, Bizerte, Tunisia
1 Department of Mathematics, Tokyo Institute of Technology, Tokyo, Japan

Correspondence: Correspondence to be sent to: Ali.Baklouti{at}fss.rnu.tn

Let H be an arbitrary closed connected subgroup of the connected, simply connected Heisenberg G = H2n+1. We present in this paper a complete description of the deformation space Formula and the moduli space Formula of adiscontinuous abelian subgroup {Gamma} of G for the homogeneous space G/H. The topological features of deformations, namely the topological stability, the rigidity, and the local rigidity are also studied.



References

  1. Baklouti A., Kédim I. On the deformation space of Clifford–Klein forms of some exponential homogeneous spaces. International Journal of Mathematics. Forthcoming.
  2. Baklouti A., Khlif F. Proper actions on some exponential solvable homogeneous spaces. International Journal of Mathematics (2005) 16(no. 9):941–55.[CrossRef][ISI]
  3. Ghys É. Déformations des structures complexes sur les espaces homogènes de Formula . Journal für die reine und angewandte Mathematik (1995) 468:113–38.[ISI]
  4. Kobayashi T. Criterion of proper action on homogeneous space of reductive type. Journal of Lie Theory (1996) 6:147–63.
  5. Kobayashi T. Deformation of compact Clifford–Klein forms of indefinite Riemannian homogeneous manifolds. Mathematische Annalen (1998) 310:394–408.
  6. Kobayashi T. Discontinuous Groups for Non-Riemannian Homogeneous Space. In: Mathematics Unlimited|2001 and Beyond—Engquist B., Schmid W., eds. (2001) New York: Springer. 723–47.
  7. Kobayashi T. Discontinuous Groups Acting on Homogeneous Spaces of Reductive Type. (1992) Proceedings of the ICM-90 Satellite Conference, 59–75. World Scientific.
  8. Kobayashi T. On discontinuous groups on homogeneous space with noncompact isotropy subgroups. Journal of Geometry and Physics (1993) 12:133–44.[CrossRef]
  9. Kobayashi T. Proper action on homogeneous space of reductive type. Mathematische Annalen (1989) 285:249–63.[CrossRef][ISI]
  10. Kobayashi T., Nasrin S. Deformation of properly discontinuous action of Formula on Formula . International Journal of Mathematics (2006) 17:1175–93.[CrossRef][ISI]
  11. Kobayashi T., Yoshino T. Compact Clifford-Klein forms of symmetric spaces—revisited. Pure and Applied Mathematics Quaterly (2005) 1(no. 3):591–663. Special issue: In Memory of Armand Borel, part 2.
  12. Palais R. S. On the existence of slices for actions of non-compact Lie groups. Annals of Mathematics (1961) 73:295–323.[CrossRef][ISI]
  13. Leptin H., Ludwig J. Unitary representation theory of exponential Lie groups. De Gruyter Expositions in Mathematics (1994) 18.
  14. Lipsman R. Proper action and a compactness condition. Journal of Lie Theory (1995) 5:25–39.
  15. Nasrin S. Criterion of proper actions for 2-step nilpotent Lie groups. Tokyo Journal of Mathematics (2001) 24(no. 2):535–43.
  16. Salein F. Varietés anti-de Sitter de dimension 3 possédant un champ de Killing non trivial. C.R. Academy of Sciences Paris (1997) 324:525–30.
  17. Yoshino T. A counterexample to Lipsman's conjecture. International Journal of Mathematics (2005) 16(no. 5):561–66.[CrossRef][ISI]
  18. Yoshino T. Criterion of proper actions for 3-step nilpotent Lie groups. International Journal of Mathematics (2007) 18(no. 7):783–95.[CrossRef][ISI]

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This Article
Right arrow Abstract Freely available
Right arrow Full Text (PDF)
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
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Right arrow Email this article to a friend
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Google Scholar
Right arrow Articles by Baklouti, A.
Right arrow Articles by Yoshino, T.
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