Sectional curvatures of ruled real hypersurfaces in a complex hyperbolic space

A ruled real hypersurface in a nonflat complex space form M˜n(c)(n≥2) of constant holomorphic sectional curvature c(≠0) is, in a word, a real hypersurface having a foliation by totally geodesic complex hyperplanes M˜n−1(c). In this paper, we investigate the sectional curvatures K of ruled real hypersurfaces in a complex hyperbolic space and show that such hypersurfaces are classified into two types with regard to the range of K.