Compact Clifford–Klein Forms – Geometry, Topology and Dynamics

NEW EXAMPLES OF COMPACT CLIFFORD-KLEIN FORMS OF HOMOGENEOUS SPACES OF SO(2, n)

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 ...

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 ...

A note on Clifford-Klein forms

We consider the problem of finding Clifford-Klein forms in a class of homogeneous spaces determined by inclusions of real Lie algebras of a special type which we call strongly regular. This class of inclusions is described in terms of their Satake diagrams. For example, the complexifications of such inclusions contain the class of subalgebras generated by automorphisms of finite order. We show ...

Relative volume comparison theorems in Finsler geometry and their applications

We establish some relative volume comparison theorems for extremal volume forms of‎ ‎Finsler manifolds under suitable curvature bounds‎. ‎As their applications‎, ‎we obtain some results on curvature and topology of Finsler manifolds‎. ‎Our results remove the usual assumption on S-curvature that is needed in the literature‎.

The Clifford-Klein Space Forms of Indefinite Metric