Abstract. First we prove a general algebraic lemma. By applying the algebraic lemma we establish a general inequality involving the Ricci curvature of an arbitrary real hypersurface in a complex hyperbolic space. We also classify real hypersurfaces with constant principal curvatures which satisfy the equality case of the inequality.
AMSclassification. Primary 53C40, 53C42; Secondary 53B25.
Keywords. Ricci curvature, shape operator, real hypersurface, algebraic lemma, tubular hypersurface, horosphere, complex hyperbolic space.