Compact Clifford-Klein forms of homogeneous spaces of SO(2,n)

Details Compact Clifford-Klein forms of homogeneous spaces of SO(2,n) Compact Clifford-Klein forms of homogeneous spaces of SO(2,n)

1999-02-08

arxiv.org/abs/math/9902050v2

Mathematics

Representation Theory

Latex2e file, 22 pages, no figures; corrected error

Scientific paper

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.

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