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

Abstract

Real hypersurfaces M²ⁿ⁻¹ of type (B) in CHⁿ(c), n ≥ 2 are known as interesting examples of Hopf hypersurfaces with constant principal curvatures. They are homogeneous in this ambient space. Moreover, the numbers of distinct principal curvatures of all real hypersurfaces of type (B) with radius r ≠ (1/$\sqrt{|c|}$) log_e(2 + $\sqrt{3}$) are 3. When r = (1/$\sqrt{|c|}$) log_e(2 + $\sqrt{3}$), the real hypersurface of type (B) has two distinct principal curvatures. The purpose of this paper is to characterize this Hopf hypersurface having two distinct constant principal curvatures.