SOME CHARACTERIZATIONS OF THE HOMOGENEOUS RULED REAL HYPERSURFACE IN A COMPLEX HYPERBOLIC SPACE

Motivated by the notion of ruled surfaces in Euclidean 3-space, we consider ruled real hypersurfaces isometrically immersed into an n-dimensional complex hyperbolic space of constant holomorphic sectional curvature c(< 0). The purpose of this expository paper is to give some geometric characterizations of the homogeneous ruled real hypersurface, that is, this ruled real hypersurface is an orbit of some subgroup of the full isometry group of the ambient space (see [2, 6, 7, 9, 10]).