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Compact Clifford-Klein forms of homogeneous spaces of SO(2,n) | | Hee Oh
; Dave Witte
; | | Date: |
8 Feb 1999 | | Subject: | Representation Theory; Differential Geometry; Group Theory MSC-class: 22E40 (Primary); 53C30 (Secondary) | math.RT math.DG math.GR | | Abstract: | 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 DG/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. | | Source: | arXiv, math.RT/9902050 | | Services: | Forum | Review | PDF | Favorites | |
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