The real hypersurface of type (B) with two distinct principal curvatures in a complex hyperbolic space (Q2452685)

A real hypersurface of type (B) in complex hyperbolic space \(\mathbb CH^n(c)\) of constant holomorphic curvature \(c<0\) is a tube around a totally real, totally geodesic \(\mathbb RH^n(c/4)\) in \(\mathbb CH^n(c)\). In [J. Reine Angew. Math. 395, 132--141 (1989; Zbl 0655.53046)] \textit{J. Berndt} classified the Hopf hypersurfaces with constant principal curvatures in \(\mathbb CH^n(c)\). These form a family of (A)-types and the (B) type. The present paper gives two sets of criteria on a connected real hypersurface of \(\mathbb CH^n(c)\), each of which is a characterizaion of a type (B) hypersurface with two distinct principal curvatures.