Rigidity of discontinuous groups for threadlike Lie groups

Fatma Khlif – GJM, Volume 1, Issue 1 (2016), 43–53.

Let G = G_n be the (n+1)-dimensional threadlike Lie group, H an arbitrary closed connected Lie subgroup of G and \Gamma \subset G an abelian discontinuous group for the homogeneous space G/H. We provide in this work an explicit description of the parameter space R(\Gamma , G, H) and of the deformation space T(\Gamma , G, H) in the particular case where n=3. Furthermore we discuss the local rigidity of T(\Gamma , G, H) and make a link with the Baklouti conjecture. This paper provides, through a concrete case study, a gentle initiation to the theory of deformations of Lie group actions

Milestones:

Received: October 2015
Published online: June 2016

Authors:

Fatma Khlif
Department of Mathematics,
Faculty of Sciences at Sfax,
Sfax University,
Route de Soukra, 1171, Sfax, Tunisia

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