Geometry of homogeneous polar foliations of complex hyperbolic spaces. (English) Zbl 1321.53066

Kubo, Akira

Hiroshima Math. J. 45, No. 1, 109-123 (2015).

Summary: Homogeneous polar foliations of complex hyperbolic spaces have been classified by J. Berndt and J. C. Díaz-Ramos [Commun. Anal. Geom. 20, No. 3, 435–454 (2012; Zbl 1262.53023)]. In this paper, we study the 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.

MSC:

53C40	Global submanifolds
53C30	Differential geometry of homogeneous manifolds
53C35	Differential geometry of symmetric spaces

Keywords:

homogeneous submanifolds; complex hyperbolic spaces; polar actions

Citations:

Zbl 1262.53023