On locally homogeneous compact pseudo-Riemannian manifolds
Tom 150 / 2017
Colloquium Mathematicum 150 (2017), 135-139 MSC: Primary 53C05; Secondary 22E40. DOI: 10.4064/cm7139s-1-2017 Opublikowany online: 11 September 2017
We are interested in the problem of the existence of compact Clifford–Klein forms of pseudo-Riemannian homogeneous spaces $G/H$ of reductive type. We give a generalization of our previous result in [Proc. Amer. Math. Soc. (2017)] with a more conceptual and simpler proof. We show that there are no solvable compact Clifford–Klein forms of pseudo-Riemannian homogeneous spaces $G/H$ with any unimodular subgroup $H$ contained in the semisimple part of the Levi factor of some parabolic subgroup.