Rigidity of Discontinuous Actions on Diamond Homogeneous Spaces | 東京大学大学院数理科学研究科理学部数学科

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Rigidity of Discontinuous Actions on Diamond Homogeneous Spaces

J. Math. Sci. Univ. Tokyo
Vol. 23 (2016), No. 2, Page 381--403.

K\'edim, Imed
Rigidity of Discontinuous Actions on Diamond Homogeneous Spaces
[Full Article (PDF)] [MathSciNet Review (HTML)] [MathSciNet Review (PDF)]

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

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