NEW EXAMPLES OF COMPACT CLIFFORD-KLEIN FORMS OF HOMOGENEOUS SPACES OF SO(2, n)
نویسنده
چکیده
Abstract. A homogeneous space G/H is said to have a compact Clifford-Klein form if there exists a discrete subgroup Γ of G that acts properly on G/H such that the quotient space Γ\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 non-compact Clifford-Klein forms of finite volume.
منابع مشابه
COMPACT CLIFFORD - KLEIN FORMS OF HOMOGENEOUS SPACES OF SO ( 2 , n )
A homogeneous space G/H is said to have a compact Clifford-Klein form if there exists a discrete subgroup Γ of G that acts properly discontinuously on G/H, such that the quotient space Γ\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 ...
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