Homogeneous polar foliations of complex hyperbolic spaces have been classified by Berndt and Dıáz-Ramos. In this paper, we study geometry of leaves of such foliations: the minimality, the parallelism of the mean curvature vectors, and the congruency of orbits. In particular, we classify minimal leaves.
"Geometry of homogeneous polar foliations of complex hyperbolic spaces." Hiroshima Math. J. 45 (1) 109 - 123, March 2015. https://doi.org/10.32917/hmj/1428365055