## Kodai Mathematical Journal

### 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/$\sqrt{|c|}$) loge(2 + $\sqrt{3}$) are 3. When r = (1/$\sqrt{|c|}$) loge(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.

#### Article information

Source
Kodai Math. J., Volume 37, Number 1 (2014), 24-33.

Dates
First available in Project Euclid: 28 March 2014

Permanent link to this document
https://projecteuclid.org/euclid.kmj/1396008247

Digital Object Identifier
doi:10.2996/kmj/1396008247

Mathematical Reviews number (MathSciNet)
MR3189513

Zentralblatt MATH identifier
1293.53072

#### Citation

Yamashita, Katsufumi; Maeda, Sadahiro. The real hypersurface of type (B) with two distinct principal curvatures in a complex hyperbolic space. Kodai Math. J. 37 (2014), no. 1, 24--33. doi:10.2996/kmj/1396008247. https://projecteuclid.org/euclid.kmj/1396008247