Example of extrinsically homogeneous real hypersurface in \(H_3(\mathbb{C})\) (Q2770039)

A submanifold in the hyperbolic complex space form \(H_n(\mathbb{C})\) is called extrinsically homogeneous if it is an orbit under a closed subgroup of the group of isometries on \(H_n(\mathbb{C})\). A Hopf hypersurface is a real hypersurface in \(H_n(\mathbb{C})\) whose vector field is principal. This paper gives an example of an extrinsically homogeneous real hypersurface in \(H_3(\mathbb{C})\) which is an orbit under a solvable Lie subgroup of the isometry group of \(H_3(\mathbb{C})\) and not a Hopf hypersurface.