DEFORMATION OF PROPERLY DISCONTINUOUS ACTIONS OF ℤk ON ℝk+1

DOI10.1142/S0129167X06003862zbMath1124.57015arXivmath/0603318OpenAlexW2138962573MaRDI QIDQ3421592

Salma Nasrin, Toshiyuki Kobayashi

Publication date: 7 February 2007

Published in: International Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0603318

zbMATH Keywords

rigiditydeformationhomogeneous spaceproper actionaffine transformationproperly discontinuous actiondiscontinuous group

Mathematics Subject Classification ID

Differential geometry of homogeneous manifolds (53C30) Deformations of general structures on manifolds (58H15) Discrete subgroups of Lie groups (22E40) Nilpotent and solvable Lie groups (22E25) Discontinuous groups of transformations (57S30)

Related Items (21)

Variants of stability of discontinuous groups for Euclidean motion groups ⋮ On the Calabi-Markus phenomenon and a rigidity theorem for Euclidean motion groups ⋮ Deformations of the discrete Heisenberg group ⋮ Stability of discontinuous groups for reduced threadlike Lie groups ⋮ Criterion of proper actions of abelian affine discontinuous groups for ℝn ⋮ Four-dimensional compact Clifford–Klein forms of pseudo-Riemannian symmetric spaces with signature (2, 2) ⋮ On the geometry of stable discontinuous subgroups acting on threadlike homogeneous spaces ⋮ Unnamed Item ⋮ Deforming discontinuous subgroups for threadlike homogeneous spaces ⋮ A local rigidity theorem for finite actions on Lie groups and application to compact extensions of \(\mathbb{R}^n\) ⋮ Linear independence of generalized Poincaré series for anti-De Sitter 3-manifolds ⋮ Stability of discontinuous groups acting on homogeneous spaces ⋮ ON THE DEFORMATION SPACE OF CLIFFORD–KLEIN FORMS OF SOME EXPONENTIAL HOMOGENEOUS SPACES ⋮ The Selberg–Weil–Kobayashi rigidity theorem: The rank one solvable case ⋮ Deformation of discontinuous subgroups acting on some nilpotent homogeneous spaces ⋮ On discontinuous subgroups acting on solvable homogeneous spaces ⋮ Deforming discontinuous groups for Heisenberg motion groups ⋮ WHEN IS THE DEFORMATION SPACE $\mathscr{T}(\Gamma, H_{2n+1}, H)$ A SMOOTH MANIFOLD? ⋮ A quantitative study of orbit counting and discrete spectrum for anti-de Sitter 3-manifolds ⋮ A splitting of local rigidity of Clifford–Klein forms of homogeneous spaces of completely solvable Lie groups ⋮ Deforming discontinuous subgroups of reduced Heisenberg groups

Cites Work

• On discontinuous groups acting on homogeneous spaces with non-compact isotropy subgroups
• On the existence of slices for actions of non-compact Lie groups
• Nonstandard Lorentz space forms
• Proper action on a homogeneous space of reductive type
• Deformation of compact Clifford-Klein forms of indefinite-Riemannian homogeneous manifolds
• Criterion of proper actions for 2-step nilpotent Lie groups
• Remarks on the cohomology of groups
• Proper actions on reductive homogeneous spaces
• Variétés anti-de Sitter de dimension 3 possédant un champ de Killing non trivial
• PROPER ACTIONS ON SOME EXPONENTIAL SOLVABLE HOMOGENEOUS SPACES

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