Rigidity of discontinuous groups for threadlike Lie groups

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

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octobre 5, 2020
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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