In this paper, we study stability for harmonic foliations on locally conformal Kähler manifolds with complex leaves. We also discuss instability for harmonic foliations on compact submanifolds immersed in Euclidean spaces and compact homogeneous spaces.
We survey results on compact Clifford–Klein forms of homogeneous spaces, with a focus on recent contributions and organized around approaches via topology, geometry and dynamics. In addition, we survey results on moduli spaces of compact forms.
