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

Hee Oh; Dave Witte

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arXiv · math/9902050

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

Hee Oh·Dave Witte

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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 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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BibTeX RIS

Hee Oh, Dave Witte. 1999-03-05. Compact Clifford-Klein forms of homogeneous spaces of SO(2,n). https://arxiv.org/abs/math/9902050

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