## Hokkaido Mathematical Journal

- Hokkaido Math. J.
- Volume 47, Number 2 (2018), 291-316.

### Characterizations of three homogeneous real hypersurfaces in a complex projective space

Makoto KIMURA and Sadahiro MAEDA

#### Abstract

In an $n$-dimensional complex hyperbolic space $\mathbb{C}H^n(c)$ of constant holomorphic sectional curvature $c (\lt 0)$, the horosphere HS, which is defined by ${\rm HS} = \lim_{r\to\infty}G(r)$, is one of nice examples in the class of real hypersurfaces. Here, $G(r)$ is a geodesic sphere of radius $r$ $(0 \lt r \lt \infty)$ in $\mathbb{C}H^n(c)$. The second author ([14]) gave a geometric characterization of HS. In this paper, motivated by this result, we study real hypersurfaces $M^{2n-1}$ isometrically immersed into an $n$-dimensional complex projective space $\mathbb{C}P^n(c)$ of constant holomorphic sectional curvature $c(\gt 0)$.

#### Article information

**Source**

Hokkaido Math. J., Volume 47, Number 2 (2018), 291-316.

**Dates**

First available in Project Euclid: 18 June 2018

**Permanent link to this document**

https://projecteuclid.org/euclid.hokmj/1529308820

**Digital Object Identifier**

doi:10.14492/hokmj/1529308820

**Mathematical Reviews number (MathSciNet)**

MR3815294

**Zentralblatt MATH identifier**

06901707

**Subjects**

Primary: 53B25: Local submanifolds [See also 53C40]

Secondary: 53C40: Global submanifolds [See also 53B25]

**Keywords**

geodesic spheres homogeneous real hypersurfaces of types (${\rm A_2})$ and type B complex projective spaces contact form exterior derivative geodesics extrinsic geodesics circles characteristic vector fields

#### Citation

KIMURA, Makoto; MAEDA, Sadahiro. Characterizations of three homogeneous real hypersurfaces in a complex projective space. Hokkaido Math. J. 47 (2018), no. 2, 291--316. doi:10.14492/hokmj/1529308820. https://projecteuclid.org/euclid.hokmj/1529308820