## Hokkaido Mathematical Journal

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

#### 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

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

Digital Object Identifier
doi:10.14492/hokmj/1529308820

Mathematical Reviews number (MathSciNet)
MR3815294

Zentralblatt MATH identifier
06901707

Subjects