## Kodai Mathematical Journal

### Ruled real hypersurfaces having the same sectional curvature as that of an ambient nonflat complex space form

#### Abstract

Ruled real hypersurfaces in a nonflat complex space form $\tilde{M}_n(c) (n ≧ 2)$ are obtained by having a one-codimensional foliation whose leaves are totally geodesic complex hypersurfaces of the ambient space. Motivated by a fact that the sectional curvature $K$ of every ruled real hypersurface $M$ in $\tilde{M}_n(c) (n ≧ 3)$ satisfies $|c/4| ≦ |K(X,Y)| ≦ |c|$ for an arbitrary pair of orthonormal vectors $X$ and $Y$ that are tangent to the leaf at each point $x$ of $M$, we study ruled real hypersurfaces having the sectional curvature $K$ with $|c/4| ≦ |K| ≦ |c|$ in $\tilde{M}_n(c)$.

#### Article information

Source
Kodai Math. J., Volume 39, Number 1 (2016), 119-128.

Dates
First available in Project Euclid: 22 March 2016

https://projecteuclid.org/euclid.kmj/1458651695

Digital Object Identifier
doi:10.2996/kmj/1458651695

Mathematical Reviews number (MathSciNet)
MR3478274

Zentralblatt MATH identifier
1343.53021

#### Citation

Maeda, Sadahiro; Tanabe, Hiromasa; Kim, Young Ho. Ruled real hypersurfaces having the same sectional curvature as that of an ambient nonflat complex space form. Kodai Math. J. 39 (2016), no. 1, 119--128. doi:10.2996/kmj/1458651695. https://projecteuclid.org/euclid.kmj/1458651695