Rigidity of Discontinuous Actions on Diamond Homogeneous Spaces
Vol. 23 (2016), No. 2, Page 381--403.
K\'edim, Imed
Rigidity of Discontinuous Actions on Diamond Homogeneous Spaces
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Abstract:
Let $G=\mathbb R^n \ltimes H_{2n+1}$ be the diamond group, $H$ a closed Lie subgroup of $G$ and $\Gamma$ a discontinuous subgroup for the homogeneous space $G/H$. We study in this paper some rigidity properties of the discontinuous action of $\Gamma$ on $G/H$. Namely, we show that the strong local rigidity fails to hold on the corresponding parameter space. In addition, when particularly $H$ is dilation-invariant, the local rigidity also fails to hold.
Keywords: Deformation spaces, diamond group, rigidity, discrete subgroup.
Mathematics Subject Classification (2010): Primary 22E25; Secondary 22G15.
Mathematical Reviews Number: MR3469003
Received: 2013-07-16
