1999/02/08 by Hee Oh, Oh, Hee, Dave Witte +1
Mathematics · #22E40 (Primary) #53C30 (Secondary) #Advanced Algebra and Geometry #Algebraic and Geometric Analysis #Differential Geometry (math.DG) #FOS: Mathematics #Group Theory (math.GR) #Mathematical Analysis and Transform Methods #Representation Theory (math.RT) #math.DG #math.GR #math.RT #msc:22E40 #msc:53C30
paper · pdf · doi:10.48550/arxiv.math/9902050
Latex2e file, 22 pages, no figures; corrected error
openalex publication_date 1999/02/08 · arxiv created 1999/03/05 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A homogeneous space G/H is said to have a compact Clifford-Klein form if there exists a discrete subgroup D of G that acts properly discontinuously on G/H, such that the quotient space D\G/H is compact. When n is even, we find every closed, connected subgroup H of G = SO(2,n), such that G/H has a compact Clifford-Klein form, but our classification is not quite complete when n is odd. The work reveals new examples of homogeneous spaces of SO(2,n) that have compact Clifford-Klein forms, if n is even. Furthermore, we show that if H is a closed, connected subgroup of G = SL(3,R), and neither H nor G/H is compact, then G/H does not have a compact Clifford-Klein form, and we also study noncompact Clifford-Klein forms of finite volume.