Compact Clifford-Klein forms of symmetric spaces -- revisited

Details Compact Clifford-Klein forms of symmetric spaces -- revisited Compact Clifford-Klein forms of symmetric spaces -- revisited

2005-09-23

arxiv.org/abs/math/0509543v1

Pure and Appl. Math. Quarterly 1 (2005), pp. 603-684, Special Issue: In Memory of Armand Borel,

Mathematics

Differential Geometry

Sperical Issue in memory of Professor Armand Borel

Scientific paper

This article discusses the existence problem of a compact quotient of a symmetric space by a properly discontinuous group with emphasis on the non-Riemannian case. Discontinuous groups are not always abundant in a homogeneous space $G/H$ if $H$ is non-compact. The first half of the article elucidates general machinery to study discontinuous groups for $G/H$, followed by the most update and complete list of symmetric spaces with/without compact quotients. In the second half, as applications of general theory, we prove: (i) there exists a 15 dimensional compact pseudo-Riemannian manifold of signature $(7,8)$ with constant curvature, (ii) there exists a compact quotient of the complex sphere of dimension 1, 3 and 7, and (iii) there exists a compact quotient of the tangential space form of signature $(p,q)$ if and only if $p$ is smaller than the Hurwitz-Radon number of $q$.

Affiliated with

Also associated with

No associations

Rating

Compact Clifford-Klein forms of symmetric spaces -- revisited does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Compact Clifford-Klein forms of symmetric spaces -- revisited, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Compact Clifford-Klein forms of symmetric spaces -- revisited will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-71232