## Kodai Mathematical Journal

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

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

Katsufumi Yamashita and Sadahiro Maeda

#### Abstract

Real hypersurfaces *M*^{2n−1} of type (B) in **C***H*^{n}(*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/) log_{e}(2 + ) are 3. When *r* = (1/) log_{e}(2 + ), 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