  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.

Representation Theory;Differential Geometry;Group Theory