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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.


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