On discontinuous groups acting on homogeneous spaces with non-compact isotropy subgroups

DOI10.1016/0393-0440(93)90011-3zbMath0815.57029OpenAlexW1965858990WikidataQ126118053 ScholiaQ126118053MaRDI QIDQ689439

Toshiyuki Kobayashi

Publication date: 10 December 1993

Published in: Journal of Geometry and Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0393-0440(93)90011-3

zbMATH Keywords

discrete subgroupCalabi-Markus phenomenoninfinite discontinuous groupsnonreductiveproperly discontinuousreductive group manifolds

Mathematics Subject Classification ID

Groups acting on specific manifolds (57S25) Differential geometry of homogeneous manifolds (53C30) Discrete subgroups of Lie groups (22E40) Discontinuous groups of transformations (57S30)

Related Items

Variants of stability of discontinuous groups for Euclidean motion groups ⋮ Intrinsic Sound of Anti-de Sitter Manifolds ⋮ A criterion of proper action on some compact extensions of ℝn and applications ⋮ On the Calabi-Markus phenomenon and a rigidity theorem for Euclidean motion groups ⋮ CRITERION OF PROPER ACTIONS FOR 3-STEP NILPOTENT LIE GROUPS ⋮ DISCONTINUOUS DUALITY THEOREM ⋮ WEAK PROPER ACTIONS ON SOLVABLE HOMOGENEOUS SPACES ⋮ Proper actions of \(\mathrm{SL}(2,\mathbb C)\) on irreducible complex symmetric spaces ⋮ Deformations of the discrete Heisenberg group ⋮ Stability of discontinuous groups for reduced threadlike Lie groups ⋮ Compact quotients of non-Archimedean rank-one 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) ⋮ Proper SL(2, ℝ)-actions on homogeneous spaces ⋮ Poincaré series for non-Riemannian locally symmetric spaces ⋮ On solvable compact Clifford-Klein forms ⋮ Properly discontinuous isometric group actions on inhomogeneous Lorentzian manifolds ⋮ On the geometry of stable discontinuous subgroups acting on threadlike homogeneous spaces ⋮ Unnamed Item ⋮ PROPER ACTIONS ON SOME EXPONENTIAL SOLVABLE HOMOGENEOUS SPACES ⋮ A COUNTEREXAMPLE TO LIPSMAN'S CONJECTURE ⋮ Deforming discontinuous subgroups for threadlike homogeneous spaces ⋮ The Volume of complete anti-de Sitter 3-manifolds ⋮ A local rigidity theorem for finite actions on Lie groups and application to compact extensions of \(\mathbb{R}^n\) ⋮ Proper actions of \(\mathrm{SL}(2,\mathbb R)\) on semisimple symmetric spaces ⋮ Stability of discontinuous groups acting on homogeneous spaces ⋮ Homogeneous space with non-virtually abelian discontinuous groups but without any proper SL(2, ℝ)-action ⋮ Cartan-decomposition subgroups of 𝑆𝑂(2,𝑛) ⋮ Completeness of certain pseudo-Riemannian (locally) symmetric spaces ⋮ A restriction on proper group actions on homogeneous spaces of reductive type ⋮ 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? ⋮ DEFORMATION OF PROPERLY DISCONTINUOUS ACTIONS OF ℤ^k ON ℝ^k+1 ⋮ A splitting of local rigidity of Clifford–Klein forms of homogeneous spaces of completely solvable Lie groups ⋮ Semisimple subalgebras in simple Lie algebras and a computational approach to the compact Clifford–Klein forms problem ⋮ Deforming discontinuous subgroups of reduced Heisenberg groups ⋮ On the fundamental group of a complete globally hyperbolic Lorentzian manifold with a lower bound for the curvature tensor

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Relativistic space forms
• The Clifford-Klein space forms of indefinite metric
• Arithmetic subgroups of algebraic groups
• The fundamental group of a compact flat Lorentz space form is virtually polycyclic
• 3-dimensional Lorentz space-forms and Seifert fiber spaces
• Kazhdan groups acting on compact manifolds
• Nonstandard Lorentz space forms
• Proper action on a homogeneous space of reductive type
• Proper actions and pseudo-Riemannian space forms
• A necessary condition for the existence of compact Clifford-Klein forms of homogeneous spaces of reductive type
• On fundamental groups of complete affinely flat manifolds
• The virtual solvability of the fundamental group of a generalized Lorentz space form
• Isotropic manifolds of indefinite metric
• The structure of complete locally affine manifolds
• On the compactness of arithmetically defined homogeneous spaces
• Compact Clifford-Klein forms of symmetric spaces
• ON A GENERALIZATION OF THE NOTION OF MANIFOLD
• Non-vanishing theorems for the cohomology of certain arithmetic quotients.